메뉴 건너뛰기




Volumn 205, Issue 2, 2003, Pages 464-524

The problem of harmonic analysis on the infinite-dimensional unitary group

Author keywords

Characters; Gelfand Tsetlin graph; Hua Pickrell measures; Infinite dimensional unitary group; Noncommutative harmonic analysis; Spectral measures

Indexed keywords


EID: 0346343169     PISSN: 00221236     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0022-1236(02)00022-8     Document Type: Article
Times cited : (92)

References (46)
  • 2
    • 0003553911 scopus 로고    scopus 로고
    • Point processes and the infinite symmetric group. Part II: Higher correlation functions
    • math/9804087
    • A. Borodin, Point processes and the infinite symmetric group. Part II: higher correlation functions, math/9804087.
    • Borodin, A.1
  • 3
    • 0003553911 scopus 로고    scopus 로고
    • Point processes and the infinite symmetric group. Part IV: Matrix Whittaker kernel
    • math/9810013
    • A. Borodin, Point processes and the infinite symmetric group. Part IV: matrix Whittaker kernel, math/9810013.
    • Borodin, A.1
  • 4
    • 0348014381 scopus 로고    scopus 로고
    • Characters of symmetric groups and correlation functions of point processes
    • (in Russian) (English translation: Funct. Anal. Appl. 34(1) (2000) 10-23)
    • A. Borodin, Characters of symmetric groups and correlation functions of point processes, Funkt. Anal. Prilozhen. 34 (1) (2000) 12-28 (in Russian) (English translation: Funct. Anal. Appl. 34(1) (2000) 10-23).
    • (2000) Funkt. Anal. Prilozhen. , vol.34 , Issue.1 , pp. 12-28
    • Borodin, A.1
  • 5
    • 0141973491 scopus 로고    scopus 로고
    • Harmonic analysis on the infinite symmetric group and the Whittaker kernel
    • (in Russian) (English translation: St. Petersburg Math. J. 12(5) (2001) 733-759)
    • A. Borodin, Harmonic analysis on the infinite symmetric group and the Whittaker kernel, Algebra Anal. 12 (5) (2000) 28-63 (in Russian) (English translation: St. Petersburg Math. J. 12(5) (2001) 733-759).
    • (2000) Algebra Anal. , vol.12 , Issue.5 , pp. 28-63
    • Borodin, A.1
  • 6
    • 0346737796 scopus 로고    scopus 로고
    • Riemann-Hilbert problem and the discrete Bessel kernel
    • math/9912093
    • A. Borodin, Riemann-Hilbert problem and the discrete Bessel kernel, Internat. Math. Res. Notices (9) (2000) 467-494; math/9912093.
    • (2000) Internat. Math. Res. Notices , Issue.9 , pp. 467-494
    • Borodin, A.1
  • 7
    • 0034390399 scopus 로고    scopus 로고
    • Asymptotics of Plancherel measures for symmetric groups
    • math/9905032
    • A. Borodin, A. Okounkov, G. Olshanski, Asymptotics of Plancherel measures for symmetric groups, J. Amer. Math. Soc. 13 (3) (2000) 481-515, math/9905032.
    • (2000) J. Amer. Math. Soc. , vol.13 , Issue.3 , pp. 481-515
    • Borodin, A.1    Okounkov, A.2    Olshanski, G.3
  • 8
    • 0003553907 scopus 로고    scopus 로고
    • Point processes and the infinite symmetric group. Part III: Fermion point processes
    • math/9804088
    • A. Borodin, G. Olshanski, Point processes and the infinite symmetric group. Part III: Fermion point processes, math/9804088.
    • Borodin, A.1    Olshanski, G.2
  • 9
    • 0032216968 scopus 로고    scopus 로고
    • Point processes and the infinite symmetric group
    • math/9810015
    • A. Borodin, G. Olshanski, Point processes and the infinite symmetric group, Math. Res. Lett. 5 (1998) 799-816, math/9810015.
    • (1998) Math. Res. Lett. , vol.5 , pp. 799-816
    • Borodin, A.1    Olshanski, G.2
  • 10
    • 0034349003 scopus 로고    scopus 로고
    • Distributions on partitions, point processes, and the hypergeometric
    • math/9904010
    • A. Borodin, G. Olshanski, Distributions on partitions, point processes, and the hypergeometric kernel, Comm. Math. Phys. 211 (2000) 335-358, math/9904010.
    • (2000) Kernel Comm. Math. Phys. , vol.211 , pp. 335-358
    • Borodin, A.1    Olshanski, G.2
  • 11
    • 0035537377 scopus 로고    scopus 로고
    • Infinite random matrices and ergodic measures
    • math-ph/0010015
    • A. Borodin, G. Olshanski, Infinite random matrices and ergodic measures, Comm. Math. Phys. 223 (2001) 87-123, math-ph/0010015.
    • (2001) Comm. Math. Phys. , vol.223 , pp. 87-123
    • Borodin, A.1    Olshanski, G.2
  • 12
    • 85030924807 scopus 로고    scopus 로고
    • Harmonic analysis on the infinite-dimensional unitary group and determinantal point processes
    • math/0109194, to appear in
    • A. Borodin, G. Olshanski, Harmonic analysis on the infinite-dimensional unitary group and determinantal point processes, math/0109194, to appear in Ann. Math.
    • Ann. Math.
    • Borodin, A.1    Olshanski, G.2
  • 13
    • 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
  • 14
    • 0001508709 scopus 로고
    • Characters and factor representations of the infinite dimensional classical groups
    • R.P. Boyer, 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
    • Boyer, R.P.1
  • 16
    • 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 (3) (1953) 367-383.
    • (1953) Trans. Amer. Math. Soc. , vol.74 , Issue.3 , pp. 367-383
    • Edrei, A.1
  • 17
    • 0003864328 scopus 로고
    • (Ed.), Bateman Manuscript Project, McGraw-Hill, New York
    • A. Erdelyi (Ed.), Higher Transcendental Functions. Bateman Manuscript Project, Vol. I, McGraw-Hill, New York, 1953.
    • (1953) Higher Transcendental Functions , vol.1
    • Erdelyi, A.1
  • 18
    • 0004209476 scopus 로고
    • Chinese Edition: Science Press, Peking, Russian Edition: IL, Moscow, 1959; English edition: Translation of Mathematical Monographs, Amer. Math. Soc., Providence, RI 1963
    • L.K. Hua, Harmonic Analysis of Functions of Several Complex Variables in the Classical Domains, Chinese Edition: Science Press, Peking, 1958; Russian Edition: IL, Moscow, 1959; English edition: Translation of Mathematical Monographs, Vol. 6, Amer. Math. Soc., Providence, RI, 1963.
    • (1958) Harmonic Analysis of Functions of Several Complex Variables in the Classical Domains , vol.6
    • Hua, L.K.1
  • 19
    • 0034288949 scopus 로고    scopus 로고
    • Random matrix theory and ζ(1/2 + it)
    • J.P. Keating, N.C. Snaith, Random matrix theory and ζ(1/2 + it), Comm. Math. Phys. 214 (2000) 57-89.
    • (2000) Comm. Math. Phys. , vol.214 , pp. 57-89
    • Keating, J.P.1    Snaith, N.C.2
  • 21
    • 0001656032 scopus 로고
    • Harmonic analysis on the infinite symmetric group. A deformation of the regular representation
    • detailed version in preparation
    • S. Kerov, G. Olshanski, A. Vershik, Harmonic analysis on the infinite symmetric group. A deformation of the regular representation, C. R. Acad. Sci. Paris Sér. I 316 (1993) 773-778 detailed version in preparation.
    • (1993) C. R. Acad. Sci. Paris Sér. I , vol.316 , pp. 773-778
    • Kerov, S.1    Olshanski, G.2    Vershik, A.3
  • 23
    • 0003516421 scopus 로고    scopus 로고
    • London Mathematical Society Monographs (New Series), Oxford University Press, Oxford, Russian edition: URSS, Moscow, 1998
    • Yu.A. Neretin, Categories of Symmetries and Infinite-Dimensional Groups, London Mathematical Society Monographs (New Series), Vol. 16, Oxford University Press, Oxford, 1996; Russian edition: URSS, Moscow, 1998.
    • (1996) Categories of Symmetries and Infinite-Dimensional Groups , vol.16
    • Neretin, Yu.A.1
  • 24
    • 0002190060 scopus 로고    scopus 로고
    • Separation of spectra in analysis of Berezin kernel
    • (in Russian) (English translation: Funct. Anal. Appl. 34 (2000) 197-207; math/9906075)
    • Yu.A. Neretin, Separation of spectra in analysis of Berezin kernel, Funkt. Anal. Prilozhen. 34 (3) (2000) 49-62 (in Russian) (English translation: Funct. Anal. Appl. 34 (2000) 197-207; math/9906075).
    • (2000) Funkt. Anal. Prilozhen. , vol.34 , Issue.3 , pp. 49-62
    • Neretin, Yu.A.1
  • 25
    • 0037104083 scopus 로고    scopus 로고
    • Hua-type integrals over unitary groups and over projective limits of unitary groups
    • math-ph/0010014
    • Yu.A. Neretin, Hua-type integrals over unitary groups and over projective limits of unitary groups, Duke Math. J. 114 (2002), 239-266, math-ph/0010014.
    • (2002) Duke Math. J. , vol.114 , pp. 239-266
    • Neretin, Yu.A.1
  • 26
    • 0037051244 scopus 로고    scopus 로고
    • 2 on Riemannian symmetric space
    • math/9911020
    • 2 on Riemannian symmetric space, J. Funct. Anal. 189 (2) (2002) 336-408, math/9911020.
    • (2002) J. Funct. Anal. , vol.189 , Issue.2 , pp. 336-408
    • Neretin, Yu.A.1
  • 27
    • 1842788768 scopus 로고    scopus 로고
    • Asymptotics of Jack polynomials as the number of variables goes to infinity
    • A. Okounkov, G. Olshanski, Asymptotics of Jack polynomials as the number of variables goes to infinity, Internat. Math. Res. Notices (13) (1998) 641-682.
    • (1998) Internat. Math. Res. Notices , Issue.13 , pp. 641-682
    • Okounkov, A.1    Olshanski, G.2
  • 28
    • 0012360416 scopus 로고
    • Unitary representations of infinite-dimensional pairs (G, K) and the formalism of R. Howe
    • G. Olshanski, Unitary representations of infinite-dimensional pairs (G, K) and the formalism of R. Howe, Soviet Math. Dokl. 27 (2) (1983) 290-294.
    • (1983) Soviet Math. Dokl. , vol.27 , Issue.2 , pp. 290-294
    • Olshanski, G.1
  • 29
    • 34249965253 scopus 로고
    • Method of holomorphic extensions in the representation theory of infinite-dimensional classical groups
    • G. Olshanski, Method of holomorphic extensions in the representation theory of infinite-dimensional classical groups, Funct. Anal. Appl. 22 (4) (1989) 273-285.
    • (1989) Funct. Anal. Appl. , vol.22 , Issue.4 , pp. 273-285
    • Olshanski, G.1
  • 30
    • 0001471212 scopus 로고
    • Unitary representations of infinite-dimensional pairs (G, K) and the formalism of R. Howe
    • A. Vershik, D. Zhelobenko (Eds.), Advanced Studies in Contemporary Mathematics, Gordon and Breach Science Publishers, New York
    • G. Olshanski, Unitary representations of infinite-dimensional pairs (G, K) and the formalism of R. Howe, in: A. Vershik, D. Zhelobenko (Eds.), Representation of Lie Groups and Related Topics, Advanced Studies in Contemporary Mathematics, Vol. 7, Gordon and Breach Science Publishers, New York, 1990, pp. 269-463.
    • (1990) Representation of Lie Groups and Related Topics , vol.7 , pp. 269-463
    • Olshanski, G.1
  • 31
    • 0000936909 scopus 로고
    • On semigroups related to infinite-dimensional groups
    • A.A. Kirillov (Ed.), Advances in Soviet Mathematics, Amer. Math. Soc., Providence, RI
    • G. Olshanski, On semigroups related to infinite-dimensional groups, in: A.A. Kirillov (Ed.), Topics in Representation Theory, Advances in Soviet Mathematics, Vol. 2, Amer. Math. Soc., Providence, RI, 1991, pp. 67-101.
    • (1991) Topics in Representation Theory , vol.2 , pp. 67-101
    • Olshanski, G.1
  • 32
    • 0003553909 scopus 로고    scopus 로고
    • Point processes and the infinite symmetric group. Part I: The general formalism and the density function
    • math/9804086
    • G. Olshanski, Point processes and the infinite symmetric group. Part I: the general formalism and the density function, math/9804086.
    • Olshanski, G.1
  • 33
    • 0003553909 scopus 로고    scopus 로고
    • Point processes and the infinite symmetric group. Part V: Analysis of the matrix Whittaker kernel
    • math/9810014
    • G. Olshanski, Point processes and the infinite symmetric group. Part V: analysis of the matrix Whittaker kernel, math/9810014.
    • Olshanski, G.1
  • 34
    • 3543017705 scopus 로고    scopus 로고
    • An introduction to harmonic analysis on the infinite symmetric group
    • A. Vershik (Ed.), Proceedings of European Summer School 2001 on Asymptotic Combinatorics with Applications to Mathematical Physics, Springer, Berlin, to appear
    • G. Olshanski, An introduction to harmonic analysis on the infinite symmetric group, in: A. Vershik (Ed.), Proceedings of European Summer School 2001 on Asymptotic Combinatorics with Applications to Mathematical Physics, Springer, Berlin, to appear.
    • Olshanski, G.1
  • 35
    • 0000236195 scopus 로고    scopus 로고
    • Ergodic unitary invariant measures on the space of infinite Hermitian matrices
    • R.L. Dobrushin, R.A. Minlos, M.A. Shubin, A.M. Vershik (Eds.), American Mathematical Society Translations, Series 2, Amer. Math. Soc., Providence, RI
    • G. Olshanski, A. Vershik, Ergodic unitary invariant measures on the space of infinite Hermitian matrices, in: R.L. Dobrushin, R.A. Minlos, M.A. Shubin, A.M. Vershik (Eds.), Contemporary Mathematical Physics, American Mathematical Society Translations, Series 2, Vol. 175, Amer. Math. Soc., Providence, RI, 1996, pp. 137-175.
    • (1996) Contemporary Mathematical Physics , vol.175 , pp. 137-175
    • Olshanski, G.1    Vershik, A.2
  • 37
    • 0000249694 scopus 로고
    • Measures on infinite dimensional Grassmann manifold
    • D. Pickrell, Measures on infinite dimensional Grassmann manifold, J. Funct. Anal. 70 (1987) 323-356.
    • (1987) J. Funct. Anal. , vol.70 , pp. 323-356
    • Pickrell, D.1
  • 38
    • 0002043076 scopus 로고
    • Die unzerlegbaren, positive-definiten Klassenfunktionen der abzählbar unendlichen, symmetrischen Gruppe
    • 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
  • 39
    • 0346122734 scopus 로고
    • Characters of infinite groups
    • Gr. Arsene, S. Strätilä, A. Verona, D. Voiculescu (Eds.), Pitman, London
    • E. Thoma, Characters of infinite groups, in: Gr. Arsene, S. Strätilä, A. Verona, D. Voiculescu (Eds.), Operator Algebras and Group Representations, Vol. 2, Pitman, London, 1984, pp. 23-32.
    • (1984) Operator Algebras and Group Representations , vol.2 , pp. 23-32
    • Thoma, E.1
  • 40
    • 0000008750 scopus 로고
    • Description of invariant measures for the actions of some infinite-dimensional groups
    • A.M. Vershik, Description of invariant measures for the actions of some infinite-dimensional groups, Sov. Math. Dokl. 15 (1974) 1396-1400.
    • (1974) Sov. Math. Dokl. , vol.15 , pp. 1396-1400
    • Vershik, A.M.1
  • 41
    • 34250241244 scopus 로고
    • Asymptotic theory of characters of the symmetric group
    • A.M. Vershik, S.V. Kerov, Asymptotic theory of characters of the symmetric group, Funct. Anal. Appl. 15 (4) (1981) 246-255.
    • (1981) Funct. Anal. Appl. , vol.15 , Issue.4 , pp. 246-255
    • Vershik, A.M.1    Kerov, S.V.2
  • 42
    • 0000724260 scopus 로고
    • Characters and factor representations of the infinite unitary group
    • A.M. Vershik, S.V. Kerov, Characters and factor representations of the infinite unitary group, Sov. Math. Dokl. 26 (1982) 570-574.
    • (1982) Sov. Math. Dokl. , vol.26 , pp. 570-574
    • Vershik, A.M.1    Kerov, S.V.2
  • 45
    • 0040354557 scopus 로고
    • Automorphic actions of compact groups on operator algebras
    • Thesis, University of Pennsylvania
    • A.J. Wassermann, Automorphic actions of compact groups on operator algebras, Thesis, University of Pennsylvania, 1981.
    • (1981)
    • Wassermann, A.J.1
  • 46
    • 0000290463 scopus 로고
    • Compact Lie groups and their Representations
    • Nauka, Moscow, (in Russian) (English translation: Amer. Math. Soc., Providence, RI 1973)
    • D.P. Zhelobenko, Compact Lie groups and their Representations, Nauka, Moscow, 1970 (in Russian) (English translation: Transl. Math. Monographs, Vol. 40, Amer. Math. Soc., Providence, RI, 1973).
    • (1970) Transl. Math. Monographs , vol.40
    • Zhelobenko, D.P.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.