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Volumn 158, Issue 3, 2004, Pages 551-642

Harmonic analysis on the infinite symmetric group

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EID: 11144268918     PISSN: 00209910     EISSN: None     Source Type: Journal    
DOI: 10.1007/s00222-004-0381-4     Document Type: Article
Times cited : (95)

References (74)
  • 1
    • 0000363076 scopus 로고
    • Exchangeability and related topics
    • Ald. Springer
    • [Ald] Aldous, D.J.: Exchangeability and related topics. Lect. Notes Math. 1117, pp. 2-199. Springer 1985
    • (1985) Lect. Notes Math. , vol.1117 , pp. 2-199
    • Aldous, D.J.1
  • 2
    • 0001955049 scopus 로고
    • Hook Young diagrams with applications to combinatorics and to representations of Lie superalgebras
    • BR
    • [BR] Berele, A., Regev, A.: Hook Young diagrams with applications to combinatorics and to representations of Lie superalgebras. Adv. Math. 64, 118-175 (1987)
    • (1987) Adv. Math. , vol.64 , pp. 118-175
    • Berele, A.1    Regev, A.2
  • 3
    • 4043080249 scopus 로고    scopus 로고
    • Multiplicative central measures on the Schur graph
    • Bor1. Representation theory, dynamical systems, combinatorial and algorithmic methods II, ed. by A.M. Vershik. St. Petersburg: Nauka (Russian)
    • [Bor1] Borodin, A.M.: Multiplicative central measures on the Schur graph. In: Representation theory, dynamical systems, combinatorial and algorithmic methods II, ed. by A.M. Vershik. Zap. Nauchn. Semin. POMI, vol. 240, pp. 44-52. St. Petersburg: Nauka 1997 (Russian); English transl. in J. Math. Sci., New York 96, 3472-3477 (1999)
    • (1997) Zap. Nauchn. Semin. POMI , vol.240 , pp. 44-52
    • Borodin, A.M.1
  • 4
    • 11144347501 scopus 로고    scopus 로고
    • English transl. New York
    • [Bor1] Borodin, A.M.: Multiplicative central measures on the Schur graph. In: Representation theory, dynamical systems, combinatorial and algorithmic methods II, ed. by A.M. Vershik. Zap. Nauchn. Semin. POMI, vol. 240, pp. 44-52. St. Petersburg: Nauka 1997 (Russian); English transl. in J. Math. Sci., New York 96, 3472-3477 (1999)
    • (1999) J. Math. Sci. , vol.96 , pp. 3472-3477
  • 5
    • 0141973491 scopus 로고    scopus 로고
    • Harmonic analysis on the infinite symmetric group and the Whittaker kernel
    • Bor2. Russian
    • [Bor2] Borodin, A.: Harmonic analysis on the infinite symmetric group and the Whittaker kernel. Algebra Anal. 12, 28-63 (2000) (Russian); English translation: St. Petersbg. Math. J. 12, 733-759 (2001)
    • (2000) Algebra Anal. , vol.12 , pp. 28-63
    • Borodin, A.1
  • 6
    • 0037727539 scopus 로고    scopus 로고
    • English translation
    • [Bor2] Borodin, A.: Harmonic analysis on the infinite symmetric group and the Whittaker kernel. Algebra Anal. 12, 28-63 (2000) (Russian); English translation: St. Petersbg. Math. J. 12, 733-759 (2001)
    • (2001) St. Petersbg. Math. J. , vol.12 , pp. 733-759
  • 7
    • 0032216968 scopus 로고    scopus 로고
    • Point processes and the infinite symmetric group
    • BO1
    • [BO1] Borodin, A., Olshanski, G.: Point processes and the infinite symmetric group. Math. Res. Lett. 5, 799-816 (1998)
    • (1998) Math. Res. Lett. , vol.5 , pp. 799-816
    • Borodin, A.1    Olshanski, G.2
  • 8
    • 3543018279 scopus 로고    scopus 로고
    • Harmonic functions on multiplicative graphs and interpolation polynomials
    • BO2, paper #R28
    • [BO2] Borodin, A., Olshanski, G.: Harmonic functions on multiplicative graphs and interpolation polynomials. Electron. J. Comb. 7 (2000), paper #R28
    • (2000) Electron. J. Comb. , vol.7
    • Borodin, A.1    Olshanski, G.2
  • 9
    • 0034349003 scopus 로고    scopus 로고
    • Distributions on partitions, point processes, and the hypergeometric kernel
    • BO3
    • [BO3] Borodin, A., Olshanski, G.: Distributions on partitions, point processes, and the hypergeometric kernel. Commun. Math. Phys. 211, 335-358 (2000)
    • (2000) Commun. Math. Phys. , vol.211 , pp. 335-358
    • Borodin, A.1    Olshanski, G.2
  • 10
    • 0035537377 scopus 로고    scopus 로고
    • Infinite random matrices and ergodic measures
    • BO4
    • [BO4] Borodin, A., Olshanski, G.: Infinite random matrices and ergodic measures. Commun. Math. Phys. 223, 87-123 (2001)
    • (2001) Commun. Math. Phys. , vol.223 , pp. 87-123
    • Borodin, A.1    Olshanski, G.2
  • 11
    • 85030924807 scopus 로고    scopus 로고
    • Harmonic analysis on the infinite-dimensional unitary group and determinantal point processes
    • BO5. arXiv:math/0109194. To appear
    • [BO5] Borodin, A., Olshanski, G.: Harmonic analysis on the infinite-dimensional unitary group and determinantal point processes. arXiv:math/0109194. To appear in Ann. Math.
    • Ann. Math.
    • Borodin, A.1    Olshanski, G.2
  • 12
    • 0003411523 scopus 로고
    • CFS. Moscow: Nauka (Russian); English translation: New York: Springer
    • [CFS] Cornfeld, I.P., Fomin, S.V., Sinai, Ya.G.: Ergodic theory. Moscow: Nauka 1980 (Russian); English translation: New York: Springer 1982
    • (1980) Ergodic Theory
    • Cornfeld, I.P.1    Fomin, S.V.2    Sinai, Ya.G.3
  • 13
    • 0040200332 scopus 로고
    • Partial exchangeability and sufficiency
    • DF (Calcutta, 1981) Calcutta: Indian Statist. Inst.
    • [DF] Diaconis, P., Freedman, D.: Partial exchangeability and sufficiency. In: Statistics: Applications and New Directions (Calcutta, 1981), pp. 205-236. Calcutta: Indian Statist. Inst. 1984
    • (1984) Statistics: Applications and New Directions , pp. 205-236
    • Diaconis, P.1    Freedman, D.2
  • 15
    • 51649133826 scopus 로고
    • On the generating functions of totally positive sequences II
    • Edr
    • [Edr] Edrei, A.: On the generating functions of totally positive sequences II. J. Anal. Math. 2, 104-109 (1952)
    • (1952) J. Anal. Math. , vol.2 , pp. 104-109
    • Edrei, A.1
  • 17
    • 0005143137 scopus 로고
    • English translation: New York, London: Academic Press
    • [GV] Gelfand, I.M., Vilenkin, N.Ya.: Some applications of harmonic analysis. Rigged Hilbert spaces (Generalized functions 4). Moscow: Fizmatgiz 1961 (Russian); English translation: Applications of harmonic analysis. New York, London: Academic Press 1964
    • (1964) Applications of Harmonic Analysis
  • 18
    • 0008059111 scopus 로고    scopus 로고
    • Representations of infinite-dimensional groups
    • Ism. Providence, RI: Amer. Math. Soc.
    • [Ism] Ismagilov, R.S.: Representations of infinite-dimensional groups. Transl. Math. Monogr. 152. Providence, RI: Amer. Math. Soc. 1996
    • (1996) Transl. Math. Monogr. , vol.152
    • Ismagilov, R.S.1
  • 19
    • 0001414233 scopus 로고
    • Measure-theoretic boundaries of Markov chains, 0-2 laws and entropy
    • Ka. ed. by M.A. Picardello, Frascati New York: Plenum
    • [Ka] Kaimanovich, V.A.: Measure-theoretic boundaries of Markov chains, 0-2 laws and entropy. In: Harmonic Analysis and Discrete Potential Theory, ed. by M.A. Picardello, pp. 145-180. Frascati 1991. New York: Plenum 1992
    • (1991) Harmonic Analysis and Discrete Potential Theory , pp. 145-180
    • Kaimanovich, V.A.1
  • 20
    • 0000616816 scopus 로고
    • On equivalence of infinite product measures
    • Kak
    • [Kak] Kakutani, S.: On equivalence of infinite product measures. Ann. Math. 49, 214-224 (1948)
    • (1948) Ann. Math. , vol.49 , pp. 214-224
    • Kakutani, S.1
  • 21
    • 0010352253 scopus 로고
    • Subordinators and the actions of permutations with quasi-invariant measure
    • Kerl. Russian
    • [Kerl] Kerov, S.V.: Subordinators and the actions of permutations with quasi-invariant measure. Zap. Nauchn. Semin. POMI, vol. 223, 181-218 (1995) (Russian); English translation: J. Math. Sci., New York 87, 4094-4117 (1997)
    • (1995) Zap. Nauchn. Semin. POMI , vol.223 , pp. 181-218
    • Kerov, S.V.1
  • 22
    • 0010394685 scopus 로고    scopus 로고
    • English translation: New York
    • [Kerl] Kerov, S.V.: Subordinators and the actions of permutations with quasi-invariant measure. Zap. Nauchn. Semin. POMI, vol. 223, 181-218 (1995) (Russian); English translation: J. Math. Sci., New York 87, 4094-4117 (1997)
    • (1997) J. Math. Sci. , vol.87 , pp. 4094-4117
  • 23
    • 0005788560 scopus 로고    scopus 로고
    • The boundary of Young lattice and random Young tableaux
    • Ker2. Formal power series and algebraic combinatorics. Providence, RI: Am. Math. Soc.
    • [Ker2] Kerov, S.V.: The boundary of Young lattice and random Young tableaux. In: Formal power series and algebraic combinatorics. DIMACS Ser. Discrete Math. Theor. Comput. Sci. 24, pp. 133-158. Providence, RI: Am. Math. Soc. 1996
    • (1996) DIMACS Ser. Discrete Math. Theor. Comput. Sci. , vol.24 , pp. 133-158
    • Kerov, S.V.1
  • 24
    • 0002298655 scopus 로고    scopus 로고
    • Anisotropic Young diagrams and Jack symmetric functions
    • Ker3. Russian
    • [Ker3] Kerov, S.V.: Anisotropic Young diagrams and Jack symmetric functions. Funkts. Anal. Prilozhen. 34, 51-64 (2000) (Russian); English translation: Funct. Anal. Appl. 34, 41-51 (2000)
    • (2000) Funkts. Anal. Prilozhen. , vol.34 , pp. 51-64
    • Kerov, S.V.1
  • 25
    • 3543047088 scopus 로고    scopus 로고
    • English translation
    • [Ker3] Kerov, S.V.: Anisotropic Young diagrams and Jack symmetric functions. Punkts. Anal. Prilozhen. 34, 51-64 (2000) (Russian); English translation: Funct. Anal. Appl. 34, 41-51 (2000)
    • (2000) Funct. Anal. Appl. , vol.34 , pp. 41-51
  • 27
    • 1842709153 scopus 로고    scopus 로고
    • The boundary of Young graph with Jack edge multiplicities
    • KOO
    • [KOO] Kerov, S., Okounkov, A., Olshanski, G.: The boundary of Young graph with Jack edge multiplicities. Int. Math. Res. Not. 4, 173-199 (1998)
    • (1998) Int. Math. Res. Not. , vol.4 , pp. 173-199
    • Kerov, S.1    Okounkov, A.2    Olshanski, G.3
  • 29
    • 0001656032 scopus 로고
    • Harmonic analysis on the infinite symmetric group. A deformation of the regular representation
    • KOV
    • [KOV] Kerov, S., Olshanski, G., Vershik, A.: Harmonic analysis on the infinite symmetric group. A deformation of the regular representation. C. R. Acad. Sci., Paris, Sér. I, Math. 316, 773-778 (1993)
    • (1993) C. R. Acad. Sci., Paris, Sér. I, Math. , vol.316 , pp. 773-778
    • Kerov, S.1    Olshanski, G.2    Vershik, A.3
  • 30
    • 0017480063 scopus 로고
    • The population structure associated with the Ewens sampling formula
    • Kin1
    • [Kin1] Kingman, J.F.C.: The population structure associated with the Ewens sampling formula. Theor. Popul. Biol. 11, 274-283 (1977)
    • (1977) Theor. Popul. Biol. , vol.11 , pp. 274-283
    • Kingman, J.F.C.1
  • 31
    • 0003523893 scopus 로고
    • Kin2. Oxford: Oxford University Press
    • [Kin2] Kingman, J.F.C.: Poisson processes. Oxford: Oxford University Press 1993
    • (1993) Poisson Processes
    • Kingman, J.F.C.1
  • 34
    • 0001038747 scopus 로고
    • On rings of operators IV
    • MvN
    • [MvN] Murray, F.J., von Neumann, J.: On rings of operators IV. Ann. Math. 44, 716-808 (1943)
    • (1943) Ann. Math. , vol.44 , pp. 716-808
    • Murray, F.J.1    Von Neumann, J.2
  • 35
    • 0004092094 scopus 로고
    • Nai. Translated from the first Russian edition. Groningen, The Netherlands: Wolters-Noordhoff Publishing
    • [Nai] Naimark, M.A.: Normed rings. Translated from the first Russian edition. Groningen, The Netherlands: Wolters-Noordhoff Publishing 1970
    • (1970) Normed Rings
    • Naimark, M.A.1
  • 36
    • 0003202643 scopus 로고    scopus 로고
    • Categories of symmetries and infinite-dimensional groups
    • Ner1. Oxford: Oxford Univ. Press Russian edition: Moscow: URSS
    • [Ner1] Neretin, Yu.A.: Categories of symmetries and infinite-dimensional groups. Lond. Math. Soc. Monogr., New Ser. 16. Oxford: Oxford Univ. Press 1996; Russian edition: Moscow: URSS 1998
    • (1996) Lond. Math. Soc. Monogr., New Ser. , vol.16
    • Neretin, Yu.A.1
  • 37
    • 0037104083 scopus 로고    scopus 로고
    • Hua type integrals over unitary groups and over projective limits of unitary groups
    • Ner2
    • [Ner2] Neretin, Yu.A.: Hua type integrals over unitary groups and over projective limits of unitary groups. Duke Math. J. 114, 239-266 (2002)
    • (2002) Duke Math. J. , vol.114 , pp. 239-266
    • Neretin, Yu.A.1
  • 38
    • 0037051244 scopus 로고    scopus 로고
    • 2 on Riemannian symmetric space
    • Ner3
    • 2 on Riemannian symmetric space. J. Funct. Anal. 189, 336-408 (2002)
    • (2002) J. Funct. Anal. , vol.189 , pp. 336-408
    • Neretin, Yu.A.1
  • 39
    • 0346129894 scopus 로고
    • Thoma's theorem and representations of infinite bisymmetric group
    • Ok1
    • [Ok1] Okounkov, A.Yu.: Thoma's theorem and representations of infinite bisymmetric group. Funct. Anal. Appl. 28, 101-107 (1994)
    • (1994) Funct. Anal. Appl. , vol.28 , pp. 101-107
    • Okounkov, A.Yu.1
  • 40
    • 0347640859 scopus 로고    scopus 로고
    • On representations of the infinite symmetric group. Representation Theory, Dynamical Systems, Combinatorial and Algorithmic Methods II
    • Ok2. A.M. Vershik. Russian
    • [Ok2] Okounkov, A.Yu.: On representations of the infinite symmetric group. Representation Theory, Dynamical Systems, Combinatorial and Algorithmic Methods II, ed. by A.M. Vershik. Zap. Nauchn. Semin. POMI, vol. 240, pp. 167-229 (1997) (Russian); English translation in J. Math. Sci., New York 96, 3550-3589 (1999)
    • (1997) Zap. Nauchn. Semin. POMI , vol.240 , pp. 167-229
    • Okounkov, A.Yu.1
  • 41
    • 0012878351 scopus 로고    scopus 로고
    • English translation, New York
    • [Ok2] Okounkov, A.Yu.: On representations of the infinite symmetric group. Representation Theory, Dynamical Systems, Combinatorial and Algorithmic Methods II, ed. by A.M. Vershik. Zap. Nauchn. Semin. POMI, vol. 240, pp. 167-229 (1997) (Russian); English translation in J. Math. Sci., New York 96, 3550-3589 (1999)
    • (1999) J. Math. Sci. , vol.96 , pp. 3550-3589
  • 42
    • 14644431524 scopus 로고    scopus 로고
    • SL(2) and z-measures
    • Ok3. Random matrix models and their applications, ed. by P.M. Bleher, A.R. Cambridge: Cambridge Univ. Press
    • [Ok3] Okounkov, A.: SL(2) and z-measures. In: Random matrix models and their applications, ed. by P.M. Bleher, A.R. Its. Math. Sci. Res. Inst. Publ. 40, pp. 407-420. Cambridge: Cambridge Univ. Press 2001
    • (2001) Its. Math. Sci. Res. Inst. Publ. , vol.40 , pp. 407-420
    • Okounkov, A.1
  • 43
    • 0003337923 scopus 로고    scopus 로고
    • Shifted Schur functions
    • OkO1. Russian
    • [OkO1] Okounkov, A., Olshanski, G.: Shifted Schur functions. Algebra Anal. 9, 73-146 (1997) (Russian); English translation: St. Petersburg Math. J. 9, 239-300 (1998)
    • (1997) Algebra Anal. , vol.9 , pp. 73-146
    • Okounkov, A.1    Olshanski, G.2
  • 44
    • 0000338772 scopus 로고    scopus 로고
    • English translation
    • [OkO1] Okounkov, A., Olshanski, G.: Shifted Schur functions. Algebra Anal. 9, 73-146 (1997) (Russian); English translation: St. Petersburg Math. J. 9, 239-300 (1998)
    • (1998) St. Petersburg Math. J. , vol.9 , pp. 239-300
  • 45
    • 0007110636 scopus 로고    scopus 로고
    • A new approach to representation theory of symmetric groups
    • OkV
    • [OkV] Okounkov, A., Vershik, A.: A new approach to representation theory of symmetric groups. Sci. Math., New Ser. 2, 581-605 (1996)
    • (1996) Sci. Math., New Ser. , vol.2 , pp. 581-605
    • Okounkov, A.1    Vershik, A.2
  • 46
    • 11144267963 scopus 로고
    • Unitary representations of the infinite-dimensional classical groups U(p, ∞), SO(p, ∞), Sp(p, ∞) and the corresponding motion groups
    • O11. Russian
    • [O11] Olshanski, G.: Unitary representations of the infinite-dimensional classical groups U(p, ∞), SO(p, ∞), Sp(p, ∞) and the corresponding motion groups. Funkts. Anal. Prilozh. 12, 20-44 (1978) (Russian); English translation: Funct. Anal. Appl. 12, 185-195 (1979)
    • (1978) Funkts. Anal. Prilozh. , vol.12 , pp. 20-44
    • Olshanski, G.1
  • 47
    • 0000785120 scopus 로고
    • English translation
    • [O11] Olshanski, G.: Unitary representations of the infinite-dimensional classical groups U(p, ∞), SO(p, ∞), Sp(p, ∞) and the corresponding motion groups. Funkts. Anal. Prilozh. 12, 20-44 (1978) (Russian); English translation: Funct. Anal. Appl. 12, 185-195 (1979)
    • (1979) Funct. Anal. Appl. , vol.12 , pp. 185-195
  • 48
    • 0012360416 scopus 로고
    • Unitary representations of infinite-dimensional pairs (G, K) and the formalism of R. Howe
    • O12
    • [O12] Olshanski, G.: Unitary representations of infinite-dimensional pairs (G, K) and the formalism of R. Howe. Soviet Math. Doklady 27, 290-294 (1983)
    • (1983) Soviet Math. Doklady , vol.27 , pp. 290-294
    • Olshanski, G.1
  • 49
    • 1842679938 scopus 로고
    • Unitaiy representations of (G, K)-pairs connected with the infinite symmetric group S(∞)
    • O13. Russian
    • [O13] Olshanski, G.: Unitaiy representations of (G, K)-pairs connected with the infinite symmetric group S(∞). Algebra Anal. 1, 178-209 (1989) (Russian); English translation: Leningrad Math. J. 1, 983-1014 (1990)
    • (1989) Algebra Anal. , vol.1 , pp. 178-209
    • Olshanski, G.1
  • 50
    • 0011022325 scopus 로고
    • English translation
    • [O13] Olshanski, G.: Unitaiy representations of (G, K)-pairs connected with the infinite symmetric group S(∞). Algebra Anal. 1, 178-209 (1989) (Russian); English translation: Leningrad Math. J. 1, 983-1014 (1990)
    • (1990) Leningrad Math. J. , vol.1 , pp. 983-1014
  • 51
    • 0001471212 scopus 로고
    • Unitary representations of infinite-dimensional pairs (G, K) and the formalism of R. Howe
    • O14. Representation of Lie Groups and Related Topics, ed. by A. Vershik, D. Zhelobenko, New York etc.: Gordon and Breach Science Publishers
    • [O14] Olshanski, G.: Unitary representations of infinite-dimensional pairs (G, K) and the formalism of R. Howe. In: Representation of Lie Groups and Related Topics, ed. by A. Vershik, D. Zhelobenko, pp. 269-463. Adv. Stud. Contemp. Math. 7. New York etc.: Gordon and Breach Science Publishers 1990
    • (1990) Adv. Stud. Contemp. Math. , vol.7 , pp. 269-463
    • Olshanski, G.1
  • 52
    • 11144301672 scopus 로고    scopus 로고
    • Point processes related to the infinite symmetric group
    • O15. The orbit method in geometry and physics: in honor of A.A. Kirillov, ed. by Ch. Duval, L. Guieu, V. Ovsienko, Boston, MA: Birkhäuser
    • [O15] Olshanski, G.: Point processes related to the infinite symmetric group. In: The orbit method in geometry and physics: in honor of A.A. Kirillov, ed. by Ch. Duval, L. Guieu, V. Ovsienko, pp. 349-393. Prog. Math. 213. Boston, MA: Birkhäuser 2003
    • (2003) Prog. Math. , vol.213 , pp. 349-393
    • Olshanski, G.1
  • 53
    • 3543017705 scopus 로고    scopus 로고
    • An introduction to harmonic analysis on the infinite symmetric group
    • O16. Asymptotic Combinatorics with Applications to Mathematical Physics, ed. by A. Vershik. Springer
    • [O16] Olshanski, G.: An introduction to harmonic analysis on the infinite symmetric group. In: Asymptotic Combinatorics with Applications to Mathematical Physics, ed. by A. Vershik. Lect. Notes Math. 1815. Springer 2003
    • (2003) Lect. Notes Math. , vol.1815
    • Olshanski, G.1
  • 54
    • 0346343169 scopus 로고    scopus 로고
    • The problem of harmonic analysis on the infinite-dimensional unitary group
    • O17
    • [O17] Olshanski, G.: The problem of harmonic analysis on the infinite-dimensional unitary group. J. Funct. Anal. 205, 464-524 (2003)
    • (2003) J. Funct. Anal. , vol.205 , pp. 464-524
    • Olshanski, G.1
  • 55
    • 11144266522 scopus 로고    scopus 로고
    • Frobenius-Schur functions
    • ORV. Studies in Memory of Issai Schur, ed. by A. Joseph, A. Melnikov, R. Rentschler, Birkhäuser
    • [ORV] Olshanski, G., Regev, A., Vershik, A.: Frobenius-Schur functions. In: Studies in Memory of Issai Schur, ed. by A. Joseph, A. Melnikov, R. Rentschler, pp. 251-300. Prog. Math. 210, Birkhäuser 2003
    • (2003) Prog. Math. , vol.210 , pp. 251-300
    • Olshanski, G.1    Regev, A.2    Vershik, A.3
  • 56
    • 0000249694 scopus 로고
    • Measures on infinite dimensional Grassmann manifold
    • Pic
    • [Pic] Pickrell, D.: Measures on infinite dimensional Grassmann manifold. J. Funct. Anal. 70, 323-356 (1987)
    • (1987) J. Funct. Anal. , vol.70 , pp. 323-356
    • Pickrell, D.1
  • 58
    • 0003737306 scopus 로고
    • Rev. Amsterdam: North-Holland
    • [Rev] Revuz, D.: Markov chains. Amsterdam: North-Holland 1984
    • (1984) Markov Chains
    • Revuz, D.1
  • 59
    • 4043128501 scopus 로고    scopus 로고
    • Multiplicative distributions on Young graph. Representation theory, dynamical systems, combinatorial and algorithmic methods II
    • Rozh. ed. by A.M. Vershik. St. Petersburg: Nauka (Russian)
    • [Rozh] Rozhkovskaya, N.A.: Multiplicative distributions on Young graph. Representation theory, dynamical systems, combinatorial and algorithmic methods II, ed. by A.M. Vershik. Zap. Nauchn. Semin. POMI, vol. 240, pp. 246-257. St. Petersburg: Nauka 1997 (Russian); English translation: J. Math. Sci., New York 96, 3600-3608 (1999)
    • (1997) Zap. Nauchn. Semin. POMI , vol.240 , pp. 246-257
    • Rozhkovskaya, N.A.1
  • 60
    • 11144291948 scopus 로고    scopus 로고
    • English translation: New York
    • [Rozh] Rozhkovskaya, N.A.: Multiplicative distributions on Young graph. Representation theory, dynamical systems, combinatorial and algorithmic methods II, ed. by A.M. Vershik. Zap. Nauchn. Semin. POMI, vol. 240, pp. 246-257. St. Petersburg: Nauka 1997 (Russian); English translation: J. Math. Sci., New York 96, 3600-3608 (1999)
    • (1999) J. Math. Sci. , vol.96 , pp. 3600-3608
  • 61
    • 0004225404 scopus 로고    scopus 로고
    • Shir. New York: Springer
    • [Shir] Shiryaev, A.: Probability. New York: Springer 1996
    • (1996) Probability
    • Shiryaev, A.1
  • 63
    • 41549090514 scopus 로고
    • Representations of AF-algebras and of the group U(∞)
    • SV. Springer
    • [SV] Strǎtilǎ, S., Voiculescu, D.: Representations of AF-algebras and of the group U(∞). Lect. Notes Math. 486. Springer 1975
    • (1975) Lect. Notes Math. , vol.486
    • Strǎtilǎ, S.1    Voiculescu, D.2
  • 64
    • 11144298540 scopus 로고    scopus 로고
    • The Ewens Sampling Formula
    • TE. ed. by S. Kotz, C.B. Read, D.L. Banks, New York: Wiley
    • [TE] Tavaré, S., Ewens, W.J.: The Ewens Sampling Formula. In: Encyclopedia of Statistical Sciences, vol. 2, ed. by S. Kotz, C.B. Read, D.L. Banks, pp. 230-234. New York: Wiley 1998
    • (1998) Encyclopedia of Statistical Sciences , vol.2 , pp. 230-234
    • Tavaré, S.1    Ewens, W.J.2
  • 65
    • 0002043076 scopus 로고
    • Die unzerlegbaren, positive-definiten Klassenfunktionen der abzählbar unendlichen, symmetrischen Gruppe
    • Tho1
    • [Tho1] Thoma, E.: Die unzerlegbaren, positive-definiten Klassenfunktionen der abzählbar unendlichen, symmetrischen Gruppe. Math. Z. 85, 40-61 (1964)
    • (1964) Math. Z. , vol.85 , pp. 40-61
    • Thoma, E.1
  • 66
    • 0346122734 scopus 로고
    • Characters of infinite groups
    • Tho2. ed. by Gr. Arsene, S. Strǎtilǎ, A. Verona, D. Voiculescu, Pitman
    • [Tho2] Thoma, E.: Characters of infinite groups. In: Operator algebras and group representations, vol. 2, ed. by Gr. Arsene, S. Strǎtilǎ, A. Verona, D. Voiculescu, pp. 23-32. Pitman 1984
    • (1984) Operator Algebras and Group Representations , vol.2 , pp. 23-32
    • Thoma, E.1
  • 67
    • 0040520724 scopus 로고
    • Description of invariant measures for the actions of some infinite-dimensional groups
    • Ver. Russian
    • [Ver] Vershik, A.: Description of invariant measures for the actions of some infinite-dimensional groups. Dokl. Akad. Nauk SSSR 218, 749-752 (1974) (Russian); English translation in Soviet Math. Doklady 15, 1396-1400 (1974)
    • (1974) Dokl. Akad. Nauk SSSR , vol.218 , pp. 749-752
    • Vershik, A.1
  • 68
    • 0000008750 scopus 로고
    • English translation
    • [Ver] Vershik, A.: Description of invariant measures for the actions of some infinite-dimensional groups. Dokl. Akad. Nauk SSSR 218, 749-752 (1974) (Russian); English translation in Soviet Math. Doklady 15, 1396-1400 (1974)
    • (1974) Soviet Math. Doklady , vol.15 , pp. 1396-1400
  • 69
    • 11144272527 scopus 로고
    • Characters and factor representations of the infinite symmetric group
    • VK1. Russian
    • [VK1] Vershik, A.M., Kerov, S.V.: Characters and factor representations of the infinite symmetric group. Dokl. Akad. Nauk SSSR 257, 1037-1040 (1981) (Russian); English translation in Soviet Math. Doklady 23, 389-392 (1981)
    • (1981) Dokl. Akad. Nauk SSSR , vol.257 , pp. 1037-1040
    • Vershik, A.M.1    Kerov, S.V.2
  • 70
    • 0002549465 scopus 로고
    • English translation
    • [VK1] Vershik, A.M., Kerov, S.V.: Characters and factor representations of the infinite symmetric group. Dokl. Akad. Nauk SSSR 257, 1037-1040 (1981) (Russian); English translation in Soviet Math. Doklady 23, 389-392 (1981)
    • (1981) Soviet Math. Doklady , vol.23 , pp. 389-392
  • 71
    • 34250241244 scopus 로고
    • Asymptotic theory of characters of the symmetric group
    • VK2
    • [VK2] Vershik, A.M., Kerov, S.V.: Asymptotic theory of characters of the symmetric group. Funct. Anal. Appl. 15, 246-255 (1981)
    • (1981) Funct. Anal. Appl. , vol.15 , pp. 246-255
    • Vershik, A.M.1    Kerov, S.V.2
  • 72
    • 0001839814 scopus 로고
    • 0-functor theory of AF-algebras. Representation of Lie groups and related topics
    • VK3. ed. by A.M. Vershik, D.P. Zhelobenko. Gordon and Breach
    • 0-functor theory of AF-algebras. Representation of Lie groups and related topics, ed. by A.M. Vershik, D.P. Zhelobenko. Adv. Stud. Contemp. Math. 7, pp. 36-114. Gordon and Breach 1990
    • (1990) Adv. Stud. Contemp. Math. , vol.7 , pp. 36-114
    • Vershik, A.M.1    Kerov, S.V.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.