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Volumn , Issue 13, 1998, Pages

Asymptotics of Jack Polynomials as the Number of Variables Goes to Infinity

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EID: 1842788768     PISSN: 10737928     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article
Times cited : (89)

References (60)
  • 1
    • 0000363076 scopus 로고
    • Exchangeability and related topics
    • École d'éte de probabilités de Saint-Flour, XIII-1983, Springer, Berlin
    • D. J. Aldous, "Exchangeability and related topics" in École d'éte de probabilités de Saint-Flour, XIII-1983, Lecture Notes in Math. 1117, Springer, Berlin, 1985, 2-199.
    • (1985) Lecture Notes in Math. , vol.1117 , pp. 2-199
    • Aldous, D.J.1
  • 2
    • 0031535563 scopus 로고    scopus 로고
    • The Calogero-Sutherland model and generalized classical polynomials
    • T. H. Baker and P. J. Forrester, The Calogero-Sutherland model and generalized classical polynomials, Comm. Math. Phys. 188 (1997), 175-216.
    • (1997) Comm. Math. Phys. , vol.188 , pp. 175-216
    • Baker, T.H.1    Forrester, P.J.2
  • 3
    • 38249024944 scopus 로고
    • A new class of symmetric polynomials defined in terms of tableaux
    • L. C. Biedenharn and J. D. Louck, A new class of symmetric polynomials defined in terms of tableaux, Adv. in Appl. Math. 10 (1989), 396-438.
    • (1989) Adv. in Appl. Math. , vol.10 , pp. 396-438
    • Biedenharn, L.C.1    Louck, J.D.2
  • 4
    • 0025091839 scopus 로고
    • Inhomogeneous basis set of symmetric polynomials defined by tableaux
    • _, Inhomogeneous basis set of symmetric polynomials defined by tableaux, Proc. Nat. Acad. Sci. U.S.A. 87 (1990), 1441-1445.
    • (1990) Proc. Nat. Acad. Sci. U.S.A. , vol.87 , pp. 1441-1445
  • 5
    • 0010961303 scopus 로고
    • Infinite traces of AF-algebras and characters of U(∞)
    • R. P. Boyer, Infinite traces of AF-algebras and characters of U(∞), J. Operator Theory 9 (1983), 205-236.
    • (1983) J. Operator Theory , vol.9 , pp. 205-236
    • Boyer, R.P.1
  • 6
    • 0001508709 scopus 로고
    • Characters and factor representations of the infinite-dimensional classical groups
    • _, Characters and factor representations of the infinite-dimensional classical groups, J. Operator Theory 28 (1992), 281-307.
    • (1992) J. Operator Theory , vol.28 , pp. 281-307
  • 7
    • 29744455506 scopus 로고
    • Solution of the one-dimensional N-body problems with quadratic and/or inversely quadratic pair potentials
    • F. Calogero, Solution of the one-dimensional N-body problems with quadratic and/or inversely quadratic pair potentials, J. Math. Phys. 12 (1971), 419-439.
    • (1971) J. Math. Phys. , vol.12 , pp. 419-439
    • Calogero, F.1
  • 8
    • 84966224610 scopus 로고
    • On the generating function of a doubly-infinite, totally positive sequence
    • A. Edrei, On the generating function of a doubly-infinite, totally positive sequence, Trans. Amer. Math. Soc. 74 (1953), 367-383.
    • (1953) Trans. Amer. Math. Soc. , vol.74 , pp. 367-383
    • Edrei, A.1
  • 9
    • 0003344023 scopus 로고
    • Basic Hypergeometric Series
    • Cambridge University Press, Cambridge
    • G. Gasper and M. Rahman, Basic Hypergeometric Series, Encyclopedia Math. Appl. 35, Cambridge University Press, Cambridge, 1990.
    • (1990) Encyclopedia Math. Appl. , vol.35
    • Gasper, G.1    Rahman, M.2
  • 10
    • 0030547104 scopus 로고    scopus 로고
    • Logarithmic convexity of push-forward measures
    • W. Graham, Logarithmic convexity of push-forward measures, Invent. Math. 123 (1996), 315-322.
    • (1996) Invent. Math. , vol.123 , pp. 315-322
    • Graham, W.1
  • 11
    • 11544254890 scopus 로고
    • Fractional statistics in one dimension: View from an exactly solvable model
    • Z. N. C. Ha, Fractional statistics in one dimension: view from an exactly solvable model, Nuclear Phys. B 435 (1995), 604-636.
    • (1995) Nuclear Phys. B , vol.435 , pp. 604-636
    • Ha, Z.N.C.1
  • 12
    • 0000648317 scopus 로고
    • A remark on the Dunkl differential-difference operators
    • Harmonic Analysis on Reductive Groups (Brunswick, ME, 1989), Birkhäuser, Boston
    • G. Heckman, "A remark on the Dunkl differential-difference operators" in Harmonic Analysis on Reductive Groups (Brunswick, ME, 1989), Progr. Math. 101, Birkhäuser, Boston, 1991, 181-191.
    • (1991) Progr. Math. , vol.101 , pp. 181-191
    • Heckman, G.1
  • 13
    • 0040499938 scopus 로고
    • The Capelli identity, the double commutant theorem, and multiplicity free actions
    • R. Howe and T. Umeda, The Capelli identity, the double commutant theorem, and multiplicity free actions, Math. Ann. 290 (1991), 565-619.
    • (1991) Math. Ann. , vol.290 , pp. 565-619
    • Howe, R.1    Umeda, T.2
  • 14
    • 0030305161 scopus 로고    scopus 로고
    • Example of a non-log-concave Duistermaat-Heckman measure
    • Y. Karshon, Example of a non-log-concave Duistermaat-Heckman measure, Math. Res. Lett. 3 (1996), 537-540.
    • (1996) Math. Res. Lett. , vol.3 , pp. 537-540
    • Karshon, Y.1
  • 15
    • 0005784688 scopus 로고
    • Generalized Hall-Littlewood symmetric functions and orthogonal polynomials
    • Representation Theory and Dynamical Systems, A. M. Vershik, ed., Amer. Math. Soc., Providence
    • S. V. Kerov, "Generalized Hall-Littlewood symmetric functions and orthogonal polynomials" in Representation Theory and Dynamical Systems, A. M. Vershik, ed., Adv. Soviet Math. 9, Amer. Math. Soc., Providence, 1992, 67-94.
    • (1992) Adv. Soviet Math. , vol.9 , pp. 67-94
    • Kerov, S.V.1
  • 18
    • 0031444933 scopus 로고    scopus 로고
    • Symmetric and non-symmetric quantum Capelli polynomials
    • F. Knop, Symmetric and non-symmetric quantum Capelli polynomials, Comment. Math. Helv. 72 (1997), 84-100.
    • (1997) Comment. Math. Helv. , vol.72 , pp. 84-100
    • Knop, F.1
  • 19
    • 0000130099 scopus 로고    scopus 로고
    • Difference equations and symmetric polynomials defined by their zeros
    • F. Knop and S. Sahi, Difference equations and symmetric polynomials defined by their zeros, IMRN (Internat. Math. Res. Notices) 1996, 473-486.
    • (1996) IMRN (Internat. Math. Res. Notices) , pp. 473-486
    • Knop, F.1    Sahi, S.2
  • 20
    • 0001230276 scopus 로고
    • Classes de Chern d'un produit tensoriel
    • Sér. A-B
    • A. Lascoux, Classes de Chern d'un produit tensoriel, C. R. Acad. Sci. Paris, Sér. A-B 286 (1978), 385-387.
    • (1978) C. R. Acad. Sci. Paris , vol.286 , pp. 385-387
    • Lascoux, A.1
  • 21
    • 0000846267 scopus 로고
    • Une formule de binôme généralisée pour les polynômes de Jack
    • M. Lassalle, Une formule de binôme généralisée pour les polynômes de Jack, C. R. Acad. Sci. Paris, Sér. I Math. 310 (1990), 253-256.
    • (1990) C. R. Acad. Sci. Paris, Sér. I Math. , vol.310 , pp. 253-256
    • Lassalle, M.1
  • 22
    • 0041010675 scopus 로고    scopus 로고
    • Single-particle Green function in the Calogero-Sutherland model for rational couplings β = p/q
    • F. Lesage, V. Pasquier, and D. Serban, Single-particle Green function in the Calogero-Sutherland model for rational couplings β = p/q, Nuclear Phys. B 466 (1996), 499-512.
    • (1996) Nuclear Phys. B , vol.466 , pp. 499-512
    • Lesage, F.1    Pasquier, V.2    Serban, D.3
  • 23
    • 0000376116 scopus 로고
    • Dynamical correlation functions in the Calogero-Sutherland model
    • _, Dynamical correlation functions in the Calogero-Sutherland model, Nuclear Phys. B 435 (1995), 585-603.
    • (1995) Nuclear Phys. B , vol.435 , pp. 585-603
  • 25
    • 0039178636 scopus 로고
    • Schur functions: Theme and variations
    • Séminaire Lotharingien de Combinatoire (Saint-Nabor, 1992), Univ. Louis Pasteur, Strasbourg
    • _, "Schur functions: theme and variations" in Séminaire Lotharingien de Combinatoire (Saint-Nabor, 1992), Publ. Inst. Rech. Math. Av. 498, Univ. Louis Pasteur, Strasbourg, 1992, 5-39.
    • (1992) Publ. Inst. Rech. Math. Av. , vol.498 , pp. 5-39
  • 26
    • 0000697008 scopus 로고
    • Quantum Berezinian and the classical Capelli identity
    • M. Nazarov, Quantum Berezinian and the classical Capelli identity, Lett. Math. Phys. 21 (1991), 123-131.
    • (1991) Lett. Math. Phys. , vol.21 , pp. 123-131
    • Nazarov, M.1
  • 27
    • 0000096598 scopus 로고    scopus 로고
    • Yangians and Capelli identities
    • Kirillov's Seminar on Representation Theory, G. Olshanski, ed., Amer. Math. Soc., Providence
    • _, "Yangians and Capelli identities" in Kirillov's Seminar on Representation Theory, G. Olshanski, ed., Amer. Math. Soc. Transl. 2, Amer. Math. Soc., Providence, 1998, 139-164.
    • (1998) Amer. Math. Soc. Transl. , vol.2 , pp. 139-164
  • 28
    • 0346129894 scopus 로고
    • Thoma's theorem and representations of the infinite bisymmetric group
    • A. Okounkov, Thoma's theorem and representations of the infinite bisymmetric group, Funct. Anal. Appl. 28 (1994), 101-107.
    • (1994) Funct. Anal. Appl. , vol.28 , pp. 101-107
    • Okounkov, A.1
  • 29
    • 0347640859 scopus 로고    scopus 로고
    • On representations of the infinite symmetric group
    • Russian
    • _, On representations of the infinite symmetric group, Zap. Nauchn. Sem. POMI 240 (1997), 167-229 (Russian); English translation to appear in J. Math. Sci.
    • (1997) Zap. Nauchn. Sem. POMI , vol.240 , pp. 167-229
  • 30
    • 1842730121 scopus 로고    scopus 로고
    • English translation to appear
    • _, On representations of the infinite symmetric group, Zap. Nauchn. Sem. POMI 240 (1997), 167-229 (Russian); English translation to appear in J. Math. Sci.
    • J. Math. Sci.
  • 31
    • 0031562876 scopus 로고    scopus 로고
    • Log-concavity of multiplicities with application to characters of U(∞)
    • _, Log-concavity of multiplicities with application to characters of U(∞), Adv. Math. 127 (1997), 258-282.
    • (1997) Adv. Math. , vol.127 , pp. 258-282
  • 32
    • 0030518235 scopus 로고    scopus 로고
    • Brunn-Minkowski inequality for multiplicities
    • _, Brunn-Minkowski inequality for multiplicities, Invent. Math. 125 (1996), 405-411.
    • (1996) Invent. Math. , vol.125 , pp. 405-411
  • 33
    • 0009318890 scopus 로고    scopus 로고
    • Multiplicities and Newton polytopes
    • Kirillov's Seminar on Representation Theory, G. Olshanski, ed., Amer. Math. Soc., Providence
    • _, "Multiplicities and Newton polytopes" in Kirillov's Seminar on Representation Theory, G. Olshanski, ed., Amer. Math. Soc. Transl. 2, Amer. Math. Soc., Providence, 1998, 231-244.
    • (1998) Amer. Math. Soc. Transl. , vol.2 , pp. 231-244
  • 34
    • 0002979621 scopus 로고    scopus 로고
    • Quantum immanants and higher Capelli identities
    • _, Quantum immanants and higher Capelli identities, Transform. Groups 1 (1996), 99-126.
    • (1996) Transform. Groups , vol.1 , pp. 99-126
  • 35
    • 1842562955 scopus 로고    scopus 로고
    • Young basis, Wick formula, and higher Capelli identities
    • _, Young basis, Wick formula, and higher Capelli identities, IMRN (Internat. Math. Res. Notices) 1996, 817-839.
    • (1996) IMRN (Internat. Math. Res. Notices) , pp. 817-839
  • 36
    • 1842780684 scopus 로고    scopus 로고
    • Macdonald polynomials: Q-Integral representation and combinatorial formula
    • (Shifted) to appear in q-alg/9605013
    • _, (Shifted) Macdonald polynomials: q-Integral representation and combinatorial formula, to appear in Comp. Math., q-alg/9605013.
    • Comp. Math.
  • 37
    • 0031287701 scopus 로고    scopus 로고
    • Binomial formula for Macdonald polynomials and applications
    • _, Binomial formula for Macdonald polynomials and applications, Math. Res. Lett. 4 (1997), 533-553.
    • (1997) Math. Res. Lett. , vol.4 , pp. 533-553
  • 38
    • 0032390708 scopus 로고    scopus 로고
    • n-type shifted Macdonald polynomials and binomial formula for Koornwinder polynomials
    • n-type shifted Macdonald polynomials and binomial formula for Koornwinder polynomials, Transform Groups 3 (1998), 181-207.
    • (1998) Transform Groups , vol.3 , pp. 181-207
  • 40
    • 0003337923 scopus 로고    scopus 로고
    • Shifted Schur functions
    • Russian
    • A. Okounkov and G. Olshanski, Shifted Schur functions, Algebra i Analiz 9 (1997), 73-146 (Russian); English trans. St. Petersburg Math. J. 9 (1998), 239-300.
    • (1997) Algebra i Analiz , vol.9 , pp. 73-146
    • Okounkov, A.1    Olshanski, G.2
  • 41
    • 0000338772 scopus 로고    scopus 로고
    • English trans.
    • A. Okounkov and G. Olshanski, Shifted Schur functions, Algebra i Analiz 9 (1997), 73-146 (Russian); English trans. St. Petersburg Math. J. 9 (1998), 239-300.
    • (1998) St. Petersburg Math. J. , vol.9 , pp. 239-300
  • 42
    • 0031286860 scopus 로고    scopus 로고
    • Shifted Jack polynomials, binomial formula, and applications
    • _, Shifted Jack polynomials, binomial formula, and applications, Math. Res. Lett. 4 (1997), 69-78.
    • (1997) Math. Res. Lett. , vol.4 , pp. 69-78
  • 43
    • 0037975038 scopus 로고    scopus 로고
    • Shifted Schur functions II
    • Kirillov's Seminar on Representation Theory, G. Olshanski, ed., Amer. Math. Soc., Providence
    • _, "Shifted Schur functions II" in Kirillov's Seminar on Representation Theory, G. Olshanski, ed., Amer. Math. Soc. Transl., 2, Amer. Math. Soc., Providence, 1998, 245-271.
    • (1998) Amer. Math. Soc. Transl. , vol.2 , pp. 245-271
  • 44
    • 0001471212 scopus 로고
    • Unitary representations of infinite-dimensional pairs (G, K) and the formalism of R. Howe
    • Representation of Lie Groups and Related Topics, A. Vershik and D. Zhelobenko, eds., Gordon and Breach Science Publishers, New York
    • G. Olshanski, "Unitary representations of infinite-dimensional pairs (G, K) and the formalism of R. Howe" in Representation of Lie Groups and Related Topics, A. Vershik and D. Zhelobenko, eds., Adv. Stud. Contemp. Math. 7, Gordon and Breach Science Publishers, New York, 1990, 269-463.
    • (1990) Adv. Stud. Contemp. Math. , vol.7 , pp. 269-463
    • Olshanski, G.1
  • 45
    • 1842679938 scopus 로고
    • Unitary representations of (G, K)-pairs connected with the infinite symmetric group S(∞)
    • Russian
    • _, Unitary representations of (G, K)-pairs connected with the infinite symmetric group S(∞), Algebra i Analiz 1 (1989), 178-209 (Russian); English translation in Leningrad Math. J. 1 (1990), 983-1014.
    • (1989) Algebra i Analiz , vol.1 , pp. 178-209
  • 46
    • 0011022325 scopus 로고
    • English translation
    • _, Unitary representations of (G, K)-pairs connected with the infinite symmetric group S(∞), Algebra i Analiz 1 (1989), 178-209 (Russian); English translation in Leningrad Math. J. 1 (1990), 983-1014.
    • (1990) Leningrad Math. J. , vol.1 , pp. 983-1014
  • 48
    • 0000236195 scopus 로고    scopus 로고
    • Ergodic unitary invariant measures on the space of infinite Hermitian matrices
    • Contemporary Mathematical Physics, R. L. Dobrushin, R. A. Minlos, M. A. Shubin, and A. M. Vershik, eds., Amer. Math. Soc., Providence
    • G. Olshanski and A. Vershik, "Ergodic unitary invariant measures on the space of infinite Hermitian matrices" in Contemporary Mathematical Physics, R. L. Dobrushin, R. A. Minlos, M. A. Shubin, and A. M. Vershik, eds., Amer. Math. Soc. Transl. Ser. 2 175, Amer. Math. Soc., Providence, 1996, 137-175.
    • (1996) Amer. Math. Soc. Transl. Ser. 2 , vol.175 , pp. 137-175
    • Olshanski, G.1    Vershik, A.2
  • 49
    • 0003377257 scopus 로고
    • Separable representations for automorphism groups of infinite symmetric spaces
    • D. Pickrell, Separable representations for automorphism groups of infinite symmetric spaces, J. Funct. Anal. 90 (1990), 1-26.
    • (1990) J. Funct. Anal. , vol.90 , pp. 1-26
    • Pickrell, D.1
  • 50
    • 0000432240 scopus 로고
    • The spectrum of certain invariant differential operators associated to a Hermitian symmetric space
    • Lie Theory and Geometry: In Honor of Bertram Kostant, J.-L. Brylinski, R. Brylinski, V. Guillemin, and V. Kac, eds., Birkhäuser, Boston
    • S. Sahi, "The spectrum of certain invariant differential operators associated to a Hermitian symmetric space" in Lie Theory and Geometry: In Honor of Bertram Kostant, J.-L. Brylinski, R. Brylinski, V. Guillemin, and V. Kac, eds., Progr. Math. 123, Birkhäuser, Boston, 1994,569-576.
    • (1994) Progr. Math. , vol.123 , pp. 569-576
    • Sahi, S.1
  • 51
    • 1842535560 scopus 로고    scopus 로고
    • Interpolation, integrality, and a generalization of Macdonald's polynomials
    • _, Interpolation, integrality, and a generalization of Macdonald's polynomials, IMRN (Internat. Math. Res. Notices) 1996, 457-471.
    • (1996) IMRN (Internat. Math. Res. Notices) , pp. 457-471
  • 52
    • 0004225404 scopus 로고    scopus 로고
    • Grad. Texts in Math. 95, Springer-Verlag, New York
    • A. Shiryaev, Probability, 2d ed., Grad. Texts in Math. 95, Springer-Verlag, New York, 1996.
    • (1996) Probability, 2d Ed.
    • Shiryaev, A.1
  • 53
    • 45249131043 scopus 로고
    • Some combinatorial properties of Jack symmetric functions
    • R. P. Stanley, Some combinatorial properties of Jack symmetric functions, Adv. Math. 77 (1989), 76-115.
    • (1989) Adv. Math. , vol.77 , pp. 76-115
    • Stanley, R.P.1
  • 54
    • 24844447275 scopus 로고
    • Exact results for a quantum many-body problem in one dimension
    • B. Sutherland, Exact results for a quantum many-body problem in one dimension, Phys. Rev. A4 (1971), 2019-2021; Phys. Rev. A5 (1972), 1372.
    • (1971) Phys. Rev. , vol.A4 , pp. 2019-2021
    • Sutherland, B.1
  • 55
    • 33646946362 scopus 로고
    • B. Sutherland, Exact results for a quantum many-body problem in one dimension, Phys. Rev. A4 (1971), 2019-2021; Phys. Rev. A5 (1972), 1372.
    • (1972) Phys. Rev. , vol.A5 , pp. 1372
  • 56
    • 0000008750 scopus 로고
    • Description of invariant measures for the actions of some infinite-dimensional groups
    • A. Vershik, Description of invariant measures for the actions of some infinite-dimensional groups, Soviet Math. Doklady 15 (1974), 1396-1400.
    • (1974) Soviet Math. Doklady , vol.15 , pp. 1396-1400
    • Vershik, A.1
  • 57
    • 34250241244 scopus 로고
    • Asymptotic theory of characters of the infinite symmetric group
    • A. M. Vershik and S. V. Kerov, Asymptotic theory of characters of the infinite 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
  • 58
    • 0000724260 scopus 로고
    • Characters and factor representations of the infinite unitary group
    • _, Characters and factor representations of the infinite unitary group, Soviet Math. Doklady 26 (1982), 570-574.
    • (1982) Soviet Math. Doklady , vol.26 , pp. 570-574


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