메뉴 건너뛰기




Volumn 7, Issue 1 R, 2000, Pages 1-39

Harmonic functions on multiplicative graphs and interpolation polynomials

Author keywords

[No Author keywords available]

Indexed keywords


EID: 3543018279     PISSN: 10778926     EISSN: None     Source Type: Journal    
DOI: 10.37236/1506     Document Type: Article
Times cited : (39)

References (61)
  • 1
    • 0001955049 scopus 로고
    • Hook Young diagrams with applications to combinatorics and to representations of Lie superalgebras
    • BR
    • [BR] A. Berele and A. Regev, Hook Young diagrams with applications to combinatorics and to representations of Lie superalgebras, Adv. Math. 64 (1987), 118-175.
    • (1987) Adv. Math. , vol.64 , pp. 118-175
    • Berele, A.1    Regev, A.2
  • 2
    • 4043080249 scopus 로고    scopus 로고
    • Multiplicative central measures on the Schur graph
    • B1, Representation theory, dynamical systems, combinatorial and algorithmical methods II (A. M. Vershik, ed.), Nauka, St. Petersburg, Russian
    • [B1] A. M. Borodin, Multiplicative central measures on the Schur graph, Representation theory, dynamical systems, combinatorial and algorithmical methods II (A. M. Vershik, ed.), Zapiski Nauchnykh Seminarov POMI 240, Nauka, St. Petersburg, 1997, pp. 44-52 (Russian); English transl. to appear in J. Math. Sci..
    • (1997) Zapiski Nauchnykh Seminarov POMI , vol.240 , pp. 44-52
    • Borodin, A.M.1
  • 3
    • 4043141066 scopus 로고    scopus 로고
    • English transl. to appear
    • [B1] A. M. Borodin, Multiplicative central measures on the Schur graph, Representation theory, dynamical systems, combinatorial and algorithmical methods II (A. M. Vershik, ed.), Zapiski Nauchnykh Seminarov POMI 240, Nauka, St. Petersburg, 1997, pp. 44-52 (Russian); English transl. to appear in J. Math. Sci..
    • J. Math. Sci.
  • 4
    • 0032576497 scopus 로고    scopus 로고
    • Biorthogonal ensembles
    • B2
    • [B2] _, Biorthogonal ensembles, Nucl. Phys. B 536 (1998), 704-732 (preprint version available via http://xxx.lanl.gov/abs/math/9804027).
    • (1998) Nucl. Phys. B , vol.536 , pp. 704-732
  • 5
    • 0032216968 scopus 로고    scopus 로고
    • Point processes and the infinite symmetric group
    • BO1
    • [BO1] A. Borodin and G. Olshanski, Point processes and the infinite symmetric group, Math. Research Lett. 5 (1998), 799-816 (preprint version available via http://xxx.lanl.gov/abs/ math/9810015).
    • (1998) Math. Research Lett. , vol.5 , pp. 799-816
    • Borodin, A.1    Olshanski, G.2
  • 6
    • 4043077394 scopus 로고    scopus 로고
    • Distributions on partitions, point processes, and the hypergeometric kernel
    • BO2, to appear
    • [BO2] _, Distributions on partitions, point processes, and the hypergeometric kernel, to appear in Comm. Math. Phys. (preprint version available via http://xxx.lanl.gov/abs/math/9904010).
    • Comm. Math. Phys.
  • 9
    • 0002357984 scopus 로고
    • Population Genetics Theory - The Past and the Future, Mathematical and statistical developments of evolutionary theory
    • Ew, (S. Lessard, ed.), Kluwer, Dordrecht
    • [Ew] W. J. Ewens, Population Genetics Theory - the Past and the Future, Mathematical and statistical developments of evolutionary theory. Proc. NATO ASI Symp. (S. Lessard, ed.), Kluwer, Dordrecht, 1990, pp. 117-228.
    • (1990) Proc. NATO ASI Symp. , pp. 117-228
    • Ewens, W.J.1
  • 10
    • 0003306028 scopus 로고
    • Harmonic analysis of functions of several complex variables in the classical domains
    • H, Amer. Math. Soc., Providence, R.I.
    • [H] L.-K. Hua, Harmonic analysis of functions of several complex variables in the classical domains, Translations of Math. Monographs, Vol. 6, Amer. Math. Soc., Providence, R.I., 1963.
    • (1963) Translations of Math. Monographs , vol.6
    • Hua, L.-K.1
  • 11
    • 4043114503 scopus 로고    scopus 로고
    • Dimension of skew shifted Young diagrams and projective representations of the infinite symmetric group
    • I1, Representation theory, dynamical systems, combinatorial and algorithmical methods II ( A. M. Vershik, ed.), Nauka, St. Petersburg, Russian
    • [I1] V. N. Ivanov, Dimension of skew shifted Young diagrams and projective representations of the infinite symmetric group, Representation theory, dynamical systems, combinatorial and algorithmical methods II (A. M. Vershik, ed.), Zapiski Nauchnykh Seminarov POMI 240, Nauka, St. Petersburg, 1997, pp. 115-135 (Russian); English transl. to appear in J. Math. Sci.
    • (1997) Zapiski Nauchnykh Seminarov POMI , vol.240 , pp. 115-135
    • Ivanov, V.N.1
  • 12
    • 4043093077 scopus 로고    scopus 로고
    • English transl. to appear
    • [I1] V. N. Ivanov, Dimension of skew shifted Young diagrams and projective representations of the infinite symmetric group, Representation theory, dynamical systems, combinatorial and algorithmical methods II (A. M. Vershik, ed.), Zapiski Nauchnykh Seminarov POMI 240, Nauka, St. Petersburg, 1997, pp. 115-135 (Russian); English transl. to appear in J. Math. Sci.
    • J. Math. Sci.
  • 13
    • 4043073098 scopus 로고    scopus 로고
    • [I2], Paper in preparation
    • [I2]_, Paper in preparation.
  • 15
    • 0005784689 scopus 로고
    • Combinatorial examples in the theory of AF-algebras
    • Ke1, Differential geometry, Lie groups and mechanics X, Russian
    • [Ke1] S. V. Kerov, Combinatorial examples in the theory of AF-algebras, Di erential geometry, Lie groups and mechanics X, Zapiski Nauchnykh Seminarov LOMI, Vol. 172, 1989, pp. 55-67 (Russian); English translation in J. Soviet Math. 59 (1992), No. 5, pp. 1063-1071.
    • (1989) Zapiski Nauchnykh Seminarov LOMI , vol.172 , pp. 55-67
    • Kerov, S.V.1
  • 16
    • 1842676876 scopus 로고
    • English translation
    • [Ke1] S. V. Kerov, Combinatorial examples in the theory of AF-algebras, Di erential geometry, Lie groups and mechanics X, Zapiski Nauchnykh Seminarov LOMI, Vol. 172, 1989, pp. 55-67 (Russian); English translation in J. Soviet Math. 59 (1992), No. 5, pp. 1063-1071.
    • (1992) J. Soviet Math. , vol.59 , Issue.5 , pp. 1063-1071
  • 17
    • 0005784688 scopus 로고
    • Generalized Hall-Littlewood symmetric functions and orthogonal polynomials
    • Ke2, Representation Theory and Dynamical Systems (A. M. Vershik, ed.), Amer. Math. Soc., Providence, R.I.
    • [Ke2] _, Generalized Hall-Littlewood symmetric functions and orthogonal polynomials, Representation Theory and Dynamical Systems (A. M. Vershik, ed.), Advances in Soviet Math. 9, Amer. Math. Soc., Providence, R.I., 1992, pp. 67-94.
    • (1992) Advances in Soviet Math. , vol.9 , pp. 67-94
  • 18
    • 0005788560 scopus 로고    scopus 로고
    • The boundary of Young lattice and random Young tableaux, Formal power series and algebraic combinatorics
    • Ke3, New Brunswick, NJ, 1994, Amer. Math. Soc., Providence, RI
    • [Ke3] _, The boundary of Young lattice and random Young tableaux, Formal power series and algebraic combinatorics (New Brunswick, NJ, 1994), DIMACS Ser. Discrete Math. Theoret. Comput. Sci., vol. 24, Amer. Math. Soc., Providence, RI, 1996, pp. 133-158.
    • (1996) DIMACS Ser. Discrete Math. Theoret. Comput. Sci. , vol.24 , pp. 133-158
  • 19
    • 0010352253 scopus 로고
    • Subordinators and permutation actions with quasi-invariant measure
    • Ke4, Representation theory, dynamical systems, combinatorial and algorithmical methods I (A. M. Vershik, ed.), Nauka, St. Petersburg, Russian
    • [Ke4] _, Subordinators and permutation actions with quasi-invariant measure, Representation theory, dynamical systems, combinatorial and algorithmical methods I (A. M. Vershik, ed.), Zapiski Nauchnykh Seminarov POMI 223, Nauka, St. Petersburg, 1995, pp. 181-218 (Russian); English transl. in J. Math. Sciences 87 (1997), No. 6.
    • (1995) Zapiski Nauchnykh Seminarov POMI , vol.223 , pp. 181-218
  • 20
    • 4043091702 scopus 로고    scopus 로고
    • English transl.
    • [Ke4] _, Subordinators and permutation actions with quasi-invariant measure, Representation theory, dynamical systems, combinatorial and algorithmical methods I (A. M. Vershik, ed.), Zapiski Nauchnykh Seminarov POMI 223, Nauka, St. Petersburg, 1995, pp. 181-218 (Russian); English transl. in J. Math. Sciences 87 (1997), No. 6.
    • (1997) J. Math. Sciences , vol.87 , Issue.6
  • 21
    • 4043070249 scopus 로고    scopus 로고
    • Anisotropic Young diagrams and Jack symmetric functions
    • Ke5, to appear
    • [Ke5] _, Anisotropic Young diagrams and Jack symmetric functions, Funct. Anal. Appl., to appear (preprint version available via http://xxx.lanl.gov/abs/ math/9712267).
    • Funct. Anal. Appl.
  • 23
    • 1842709153 scopus 로고    scopus 로고
    • The boundary of Young graph with Jack edge multiplicities
    • KOO
    • [KOO] S. Kerov, A. Okounkov, G. Olshanski, The boundary of Young graph with Jack edge multiplicities, Intern. Math. Res. Notices (1998), No.4, 173-199.
    • (1998) Intern. Math. Res. Notices , Issue.4 , pp. 173-199
    • Kerov, S.1    Okounkov, A.2    Olshanski, G.3
  • 24
    • 0001656032 scopus 로고
    • Harmonic analysis on the infinite symmetric group. A deformation of the regular representation
    • KOV
    • [KOV] S. Kerov, G. Olshanski, A. Vershik, Harmonic analysis on the infinite symmetric group. A deformation of the regular representation, Comptes Rend. Acad. Sci. Paris, Sér. I 316(1993), 773-778.
    • (1993) Comptes Rend. Acad. Sci. Paris, Sér. I , vol.316 , pp. 773-778
    • Kerov, S.1    Olshanski, G.2    Vershik, A.3
  • 25
    • 27744507962 scopus 로고
    • Characters, factor representations and K-functor of the infinite symmetric group
    • KV1, Operator algebras and group representations, Vol. II (Neptun, 1980), Pitman, Boston-London
    • [KV1] S. V. Kerov and A. M Vershik, Characters, factor representations and K-functor of the infinite symmetric group., Operator algebras and group representations, Vol. II (Neptun, 1980), Monographs Stud. Math. 18, Pitman, Boston-London, 1984, pp. 23-32.
    • (1984) Monographs Stud. Math. , vol.18 , pp. 23-32
    • Kerov, S.V.1    Vershik, A.M.2
  • 26
    • 0001839814 scopus 로고
    • 0-functor theory of AF-algebras
    • KV2, Representation of Lie groups and related topics (A. M. Vershik and D. P. Zhelobenko, eds.), Gordon and Breach
    • 0-functor theory of AF-algebras, Representation of Lie groups and related topics (A. M. Vershik and D. P. Zhelobenko, eds.), Adv. Stud. Contemp. Math. 7, Gordon and Breach, 1990, pp. 36-114.
    • (1990) Adv. Stud. Contemp. Math. , vol.7 , pp. 36-114
    • Kerov, S.1    Vershik, A.2
  • 27
    • 0001503633 scopus 로고
    • Random partitions in population genetics
    • Ki1
    • [Ki1] J. F. C. Kingman, Random partitions in population genetics, Proc. Roy. Soc. London A. 361 (1978), 1-20.
    • (1978) Proc. Roy. Soc. London A. , vol.361 , pp. 1-20
    • Kingman, J.F.C.1
  • 28
    • 84927129559 scopus 로고
    • The representation of partition structures
    • Ki2
    • [Ki2] _, The representation of partition structures, J. London Math. Soc. 18 (1978), 374-380.
    • (1978) J. London Math. Soc. , vol.18 , pp. 374-380
  • 29
    • 0003523893 scopus 로고
    • Ki3 _, Oxford University Press
    • [Ki3] , Poisson processes, Oxford University Press, 1993.
    • (1993) Poisson Processes
  • 30
    • 0000130099 scopus 로고    scopus 로고
    • Difference equations and symmetric polynomials defined by their zeros
    • KS
    • [KS] F. Knop and S. Sahi, Difference equations and symmetric polynomials defined by their zeros, Internat. Math. Res. Notices (1996), no. 10, 473-486.
    • (1996) Internat. Math. Res. Notices , Issue.10 , pp. 473-486
    • Knop, F.1    Sahi, S.2
  • 32
    • 1842676873 scopus 로고
    • Projective representations of the infinite symmetric group
    • N, , Representation theory and dynamical systems (A. M. Vershik, ed.), Amer. Math. Soc., Providence, RI
    • [N] M. Nazarov, Projective representations of the infinite symmetric group, Representation theory and dynamical systems (A. M. Vershik, ed.), Adv. Soviet Math., 9, Amer. Math. Soc., Providence, RI, 1992, pp. 115-130.
    • (1992) Adv. Soviet Math. , vol.9 , pp. 115-130
    • Nazarov, M.1
  • 33
    • 0002979621 scopus 로고    scopus 로고
    • Quantum immanants and higher Capelli identities
    • Ok1
    • [Ok1] _, Quantum immanants and higher Capelli identities, Transformation Groups 1 (1996), no. 1-2, 99-126.
    • (1996) Transformation Groups , vol.1 , Issue.1-2 , pp. 99-126
  • 34
    • 0038839972 scopus 로고    scopus 로고
    • (Shifted) Macdonald polynomials: q-Integral representation and combinatorial formula
    • Ok2
    • [Ok2] _, (Shifted) Macdonald polynomials: q-Integral representation and combinatorial formula, Comp. Math. 12 (1998), 147-182.
    • (1998) Comp. Math. , vol.12 , pp. 147-182
  • 35
    • 0346129894 scopus 로고
    • Thoma's theorem and representations of infinite bisymmetric group
    • Ok3
    • [Ok3] _, Thoma's theorem and representations of infinite bisymmetric group, Funct. Anal. Appl. 28 (1994), no. 2, 101-107.
    • (1994) Funct. Anal. Appl. , vol.28 , Issue.2 , pp. 101-107
  • 36
    • 0031287701 scopus 로고    scopus 로고
    • Binomial formula for Macdonald polynomials
    • Ok4
    • [Ok4] _, Binomial formula for Macdonald polynomials, Math. Res. Lett. 4 (1997), 533-553.
    • (1997) Math. Res. Lett. , vol.4 , pp. 533-553
  • 37
    • 0003337923 scopus 로고    scopus 로고
    • Shifted Schur functions
    • OO, Russian
    • [OO] A. Okounkov and G. Olshanski, Shifted Schur functions, Algebra i Analiz 9 (1997), no. 2, 73-146 (Russian); English translation: St. Petersburg Math. J. 9 (1998), no. 2, 239-300.
    • (1997) Algebra I Analiz , vol.9 , Issue.2 , pp. 73-146
    • Okounkov, A.1    Olshanski, G.2
  • 38
    • 0000338772 scopus 로고    scopus 로고
    • English translation: St. Petersburg
    • [OO] A. Okounkov and G. Olshanski, Shifted Schur functions, Algebra i Analiz 9 (1997), no. 2, 73-146 (Russian); English translation: St. Petersburg Math. J. 9 (1998), no. 2, 239-300.
    • (1998) Math. J. , vol.9 , Issue.2 , pp. 239-300
  • 39
    • 0031286860 scopus 로고    scopus 로고
    • Shifted Jack polynomials, binomial formula, and applications, q-alg/9608020
    • OO2
    • [OO2] _, Shifted Jack polynomials, binomial formula, and applications, q-alg/9608020, Math. Res. Lett. 4 (1997), 69-78.
    • (1997) Math. Res. Lett. , vol.4 , pp. 69-78
  • 40
    • 0007110636 scopus 로고    scopus 로고
    • A new approach to representation theory of symmetric groups
    • OV
    • [OV] A. Okounkov and A. Vershik, A new approach to representation theory of symmetric groups, Selecta Math. (N.S.) 2 (1996), no. 4, 581-605.
    • (1996) Selecta Math. (N.S.) , vol.2 , Issue.4 , pp. 581-605
    • Okounkov, A.1    Vershik, A.2
  • 41
    • 1842679938 scopus 로고
    • Unitary representations of (G,K)-pairs connected with the infinite symmetric group S(∞)
    • Ol, Russian
    • [Ol] G. I. Olshanskii, Unitary representations of (G,K)-pairs connected with the infinite symmetric group S(∞), Algebra i Analiz 1 (1989), no. 4, 178-209 (Russian); English translation in Leningrad Math. J. 1 (1990), no. 4, 983-1014.
    • (1989) Algebra I Analiz , vol.1 , Issue.4 , pp. 178-209
    • Olshanskii, G.I.1
  • 42
    • 0011022325 scopus 로고
    • English translation
    • [Ol] G. I. Olshanskii, Unitary representations of (G,K)-pairs connected with the infinite symmetric group S(∞), Algebra i Analiz 1 (1989), no. 4, 178-209 (Russian); English translation in Leningrad Math. J. 1 (1990), no. 4, 983-1014.
    • (1990) Leningrad Math. J. , vol.1 , Issue.4 , pp. 983-1014
  • 49
    • 0003363020 scopus 로고
    • Lectures on Choquet's theorem
    • Ph, Princeton, NJ
    • [Ph] R. R. Phelps, Lectures on Choquet's theorem, Van Nostrand mathematical studies, Vol. 7, Princeton, NJ, 1966.
    • (1966) Van Nostrand Mathematical Studies , vol.7
    • Phelps, R.R.1
  • 50
    • 0040801503 scopus 로고
    • The two-parameter generalization of Ewens' random partition structure
    • Pi
    • [Pi] J. Pitman, The two-parameter generalization of Ewens' random partition structure, Univ. Calif. Berkeley, Dept. Stat. Technical Report 345 (1992), 1-23.
    • (1992) Univ. Calif. Berkeley, Dept. Stat. Technical Report , vol.345 , pp. 1-23
    • Pitman, J.1
  • 51
    • 0031534984 scopus 로고    scopus 로고
    • The two-parameter Poisson-Dirichlet distribution derived from a stable subordinator
    • PY
    • [PY] J. Pitman and M. Yor, The two-parameter Poisson-Dirichlet distribution derived from a stable subordinator, Ann. Prob. 25 (1997), 855-900.
    • (1997) Ann. Prob. , vol.25 , pp. 855-900
    • Pitman, J.1    Yor, M.2
  • 54
    • 0040711880 scopus 로고
    • On a Jacobi-Trudi identity for supersymmetric polynomials
    • PT
    • [PT] P. Pragacz and A. Thorup, On a Jacobi-Trudi identity for supersymmetric polynomials, Adv. Math. (1992f), 8-17.
    • (1992) Adv. Math. , pp. 8-17
    • Pragacz, P.1    Thorup, A.2
  • 56
    • 4043128501 scopus 로고    scopus 로고
    • Multiplicative distributions on Young graph, Representation theory, dynamical systems, combinatorial and algorithmical methods II
    • Ro, A. M. Vershik, ed., Nauka, St. Petersburg, Russian
    • [Ro] N. A. Rozhkovskaya, Multiplicative distributions on Young graph, Representation theory, dynamical systems, combinatorial and algorithmical methods II (A. M. Vershik, ed.), Zapiski Nauchnykh Seminarov POMI 240, Nauka, St. Petersburg, 1997, pp. 246-257 (Russian); English transl. to appear in J. Math. Sci.
    • (1997) Zapiski Nauchnykh Seminarov POMI , vol.240 , pp. 246-257
    • Rozhkovskaya, N.A.1
  • 57
    • 4043090236 scopus 로고    scopus 로고
    • English transl. to appear
    • [Ro] N. A. Rozhkovskaya, Multiplicative distributions on Young graph, Representation theory, dynamical systems, combinatorial and algorithmical methods II (A. M. Vershik, ed.), Zapiski Nauchnykh Seminarov POMI 240, Nauka, St. Petersburg, 1997, pp. 246-257 (Russian); English transl. to appear in J. Math. Sci.
    • J. Math. Sci.
  • 58
    • 0000432240 scopus 로고
    • The spectrum of certain invariant di erential operators associated to a Hermitian symmetric space
    • S, Lie Theory and Geometry: In Honor of Bertram Kostant (J.-L. Brylinski, R. Brylinski, V. Guillemin, V. Kac, eds.), Birkhäuser, Boston, Basel
    • [S] S. Sahi, The spectrum of certain invariant di erential operators associated to a Hermitian symmetric space, Lie Theory and Geometry: In Honor of Bertram Kostant (J.-L. Brylinski, R. Brylinski, V. Guillemin, V. Kac, eds.), Progress in Mathematics 123, Birkhäuser, Boston, Basel, 1994, pp. 569-576.
    • (1994) Progress in Mathematics , vol.123 , pp. 569-576
    • Sahi, S.1
  • 59
    • 0002043076 scopus 로고
    • Die unzerlegbaren, positive-definiten Klassenfunktionen der abzählbar unendlichen, symmetrischen Gruppe
    • T
    • [T] E. Thoma, Die unzerlegbaren, positive-definiten Klassenfunktionen der abzählbar unendlichen, symmetrischen Gruppe, Math. Zeitschr. 85 (1964), 40-61.
    • (1964) Math. Zeitschr. , vol.85 , pp. 40-61
    • Thoma, E.1
  • 60
    • 34250241244 scopus 로고
    • Asymptotic theory of characters of the symmetric group
    • VK
    • [VK] A. M. Vershik, S. V. Kerov, Asymptotic theory of characters of the symmetric group, Funct. Anal. Appl. 15 (1981), 246-255.
    • (1981) Funct. Anal. Appl. , vol.15 , pp. 246-255
    • Vershik, A.M.1    Kerov, S.V.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.