메뉴 건너뛰기




Volumn 195, Issue 2, 2002, Pages 306-349

Branching coefficients of holomorphic representations and Segal-Bargmann transform

Author keywords

Bounded symmetric domains; Branching rule; Cayley identity; Highst weigth represenatations; Holomorphic discrete series; Jack symmetric polynomials; Jordan pairs; Orthogonal polynomials; Real bounded symmetric domains

Indexed keywords


EID: 0037058486     PISSN: 00221236     EISSN: None     Source Type: Journal    
DOI: 10.1006/jfan.2002.3957     Document Type: Article
Times cited : (31)

References (39)
  • 1
    • 0000629216 scopus 로고
    • Certain hypergeometric series related to the root system BC
    • R. Beerends and E. Opdam, Certain hypergeometric series related to the root system BC, Trans. AMS. 339 (1993), 581-609.
    • (1993) Trans. AMS , vol.339 , pp. 581-609
    • Beerends, R.1    Opdam, E.2
  • 2
    • 0001634909 scopus 로고
    • A unification of the Knizhnik Zamolodchikov and Dunkl operators via affine Hecke algebras
    • I. Cherednik, A unification of the Knizhnik Zamolodchikov and Dunkl operators via affine Hecke algebras, Invent. Math. 106 (1991), 411-432.
    • (1991) Invent. Math. , vol.106 , pp. 411-432
    • Cherednik, I.1
  • 3
    • 0004334138 scopus 로고    scopus 로고
    • Segal-Bargmann transform on Hermitian symmetric spaces
    • preprint
    • M. Davidson, G. Olafsson, and G. Zhang, Segal-Bargmann transform on Hermitian symmetric spaces, preprint.
    • Davidson, M.1    Olafsson, G.2    Zhang, G.3
  • 4
    • 84963950040 scopus 로고
    • Differential -difference operators associated to reflection groups
    • C. F. Dunkl, Differential -difference operators associated to reflection groups, Trans. AMS 311 (1989), 167-183.
    • (1989) Trans. AMS , vol.311 , pp. 167-183
    • Dunkl, C.F.1
  • 5
    • 0001195479 scopus 로고
    • Integral kernels with reflection group invariance
    • C. F. Dunkl, Integral kernels with reflection group invariance, Canadian J. Math. 43 (1991), 1213-1227.
    • (1991) Canadian J. Math. , vol.43 , pp. 1213-1227
    • Dunkl, C.F.1
  • 6
    • 0032186752 scopus 로고    scopus 로고
    • Orthogonal polynomials of types A and B and related Calogero models
    • C. F. Dunkl, Orthogonal polynomials of types A and B and related Calogero models, Comm. Math. Phys. 197 (1998), 451-487.
    • (1998) Comm. Math. Phys. , vol.197 , pp. 451-487
    • Dunkl, C.F.1
  • 7
    • 0001768923 scopus 로고
    • Function spaces and reproducing kernels on bounded symmetric domains
    • J. Faraut and A. Koranyi, Function spaces and reproducing kernels on bounded symmetric domains, J. Funct. Anal. 88 (1990), 64-89.
    • (1990) J. Funct. Anal. , vol.88 , pp. 64-89
    • Faraut, J.1    Koranyi, A.2
  • 8
    • 33645846237 scopus 로고
    • "Analysis on Symmetric Cones"
    • Oxford Univ. Press, Oxford
    • J. Faraut and A. Koranyi, "Analysis on Symmetric Cones," Oxford Univ. Press, Oxford, 1994.
    • (1994)
    • Faraut, J.1    Koranyi, A.2
  • 9
    • 85031363353 scopus 로고
    • Causal semisimple symmetric spaces, the geometry and harmonic analysis "Semigroups in Algebra Geometry and Analysis"
    • (Lawson Hofmann and Vinberg, Eds.), De Gruyter, Berlin
    • J. Faraut and G. Olafsson, Causal semisimple symmetric spaces, the geometry and harmonic analysis, in "Semigroups in Algebra Geometry and Analysis" (Lawson Hofmann and Vinberg, Eds.), De Gruyter, Berlin, 1995.
    • (1995)
    • Faraut, J.1    Olafsson, G.2
  • 10
    • 0000648317 scopus 로고
    • A remark on the Dunkl differential-difference operators
    • "Harmonic Analysis on Reductive Groups" (Brunswick, ME, 1989), Progress in Mathematics, Birkhäuser, Boston
    • G. J. Heckman,, A remark on the Dunkl differential-difference operators, in "Harmonic Analysis on Reductive Groups" (Brunswick, ME, 1989), Progress in Mathematics, Vol. 101, pp. 181-191, Birkhäuser, Boston, 1991.
    • (1991) , vol.101 , pp. 181-191
    • Heckman, G.J.1
  • 11
    • 0003563179 scopus 로고
    • "Differential Geometry and Symmetric Spaces"
    • Academic Press, New York, London
    • S. Helgason, "Differential Geometry and Symmetric Spaces," Academic Press, New York, London, 1978.
    • (1978)
    • Helgason, S.1
  • 12
    • 0003670714 scopus 로고
    • "Groups and Geometric Analysis"
    • Academic Press, New York, London
    • S. Helgason, "Groups and Geometric Analysis," Academic Press, New York, London, 1984.
    • (1984)
    • Helgason, S.1
  • 13
    • 0010553238 scopus 로고    scopus 로고
    • "Causal Symmetric Spaces, Geometry and Harmonic Analysis"
    • Academic Press, New York
    • J. Hilgert and G. Ólafsson, "Causal Symmetric Spaces, Geometry and Harmonic Analysis," Perspectives in Mathematics, Vol. 18, Academic Press, New York 1996.
    • (1996) Perspectives in Mathematics , vol.18
    • Hilgert, J.1    Ólafsson, G.2
  • 14
    • 0038900143 scopus 로고
    • The first fundamental theorem of invariant theory and spherical subgroups
    • "Algebraic Groups and their Generalizations: Classical Methods" (University Park, PA, 1991), Part I, Proceedings Symposium on Pure Mathematics Providence, RI
    • R. Howe, The first fundamental theorem of invariant theory and spherical subgroups, in "Algebraic Groups and their Generalizations: Classical Methods" (University Park, PA, 1991), Part I, Proceedings Symposium on Pure Mathematics, Vol. 56, Amer. Math. Soc., Providence, RI, 1994.
    • (1994) Amer. Math. Soc. , vol.56
    • Howe, R.1
  • 15
    • 0040499938 scopus 로고
    • The Capelli identity, the double commutant theorem, and multiplicity free action
    • R. Howe and T. Umeda, The Capelli identity, the double commutant theorem, and multiplicity free action, Math. Ann. 290 (1991), 565-619.
    • (1991) Math. Ann. , vol.290 , pp. 565-619
    • Howe, R.1    Umeda, T.2
  • 16
    • 0003214977 scopus 로고
    • "Harmonic Analysis of Functions of Several Complex Variables in the Classical Domains"
    • Providence, RI
    • L. K. Hua, "Harmonic Analysis of Functions of Several Complex Variables in the Classical Domains," Amer. Math. Soc., Providence, RI, 1963.
    • (1963) Amer. Math. Soc.
    • Hua, L.K.1
  • 17
    • 4243460339 scopus 로고    scopus 로고
    • Multiplicity-free restrictions of unitary highest weight modules for reductive symmetric pairs
    • preprint
    • T. Kobayashi, Multiplicity-free restrictions of unitary highest weight modules for reductive symmetric pairs, preprint.
    • Kobayashi, T.1
  • 18
    • 0011935102 scopus 로고    scopus 로고
    • Multiplicity-free branching laws for unitary highest weight modules, in "Proceedings of the Symposium on Representation Theory"
    • Saga, Kyushu, 1997 (K. Mimachi, Ed.)
    • T. Kobayashi, Multiplicity-free branching laws for unitary highest weight modules, in "Proceedings of the Symposium on Representation Theory," Saga, Kyushu, 1997 (K. Mimachi, Ed.), pp. 8-17, 1997.
    • (1997) , pp. 8-17
    • Kobayashi, T.1
  • 19
    • 0000776677 scopus 로고
    • Sphärische Untergruppen in kompakten zusammenhängenden Liegruppen
    • M. Krämer, Sphärische Untergruppen in kompakten zusammenhängenden Liegruppen, Compositio Math. 38 (1979), 129-153.
    • (1979) Compositio Math. , vol.38 , pp. 129-153
    • Krämer, M.1
  • 20
    • 0000402823 scopus 로고    scopus 로고
    • Coefficients binomiaux généralisés et polynômes de Macdonald
    • M. Lassalle, Coefficients binomiaux généralisés et polynômes de Macdonald, J. Funct. Anal. 158 (1998), 289-324.
    • (1998) J. Funct. Anal. , vol.158 , pp. 289-324
    • Lassalle, M.1
  • 21
    • 0003480853 scopus 로고
    • "Bounded Symmetric Domains and Jordan Pairs"
    • Univ. of California, Irvine
    • O. Loos, "Bounded Symmetric Domains and Jordan Pairs," Univ. of California, Irvine, 1977.
    • (1977)
    • Loos, O.1
  • 22
    • 0011969775 scopus 로고    scopus 로고
    • "Hypergeometric Functions"
    • Lecture Notes, unpublished
    • I. G. Macdonald, "Hypergeometric Functions," Lecture Notes, unpublished.
    • Macdonald, I.G.1
  • 24
    • 0011972530 scopus 로고    scopus 로고
    • Matrix analogs of the integral B(α, π - α) and Plancherel formula for Berezin kernel representations
    • preprint Math.RT/9905045
    • Yu. Neretin, Matrix analogs of the integral B(α, π - α) and Plancherel formula for Berezin kernel representations, preprint, 1999, Math.RT/9905045.
    • (1999)
    • Neretin, Yu.1
  • 25
    • 0011965397 scopus 로고
    • Symmetric spaces of hermitian type
    • G. Ólafsson, Symmetric spaces of hermitian type, Differential Geom. Appl. 1 (1991), 195-233.
    • (1991) Differential Geom. Appl. , vol.1 , pp. 195-233
    • Ólafsson, G.1
  • 26
    • 0001884902 scopus 로고    scopus 로고
    • Generalizations of the Bargmann transform "Lie Theory and its Applications in Physics, Proceedings of the International Workshop"
    • Clausthal, Germany, August 14-17, 1995 (H.-D. Doebner et al., Eds.), World Scientific, Singapore
    • G. Ólafsson and B. Örsted, Generalizations of the Bargmann transform, in "Lie Theory and its Applications in Physics, Proceedings of the International Workshop," Clausthal, Germany, August 14-17, 1995 (H.-D. Doebner et al., Eds.), pp. 3-14, World Scientific, Singapore, 1996.
    • (1996) , pp. 3-14
    • Ólafsson, G.1    Örsted, B.2
  • 27
    • 0000775503 scopus 로고
    • Dunkl operators, Bessel functions and the discriminant of a finite Coxeter group
    • E. Opdam, Dunkl operators, Bessel functions and the discriminant of a finite Coxeter group, Compositio Math. 85 (1993), 333-373.
    • (1993) Compositio Math. , vol.85 , pp. 333-373
    • Opdam, E.1
  • 28
    • 0000221732 scopus 로고
    • Weyl quantization and tensor products of Fock and Bergman spaces
    • B. Ørsted and G. Zhang, Weyl quantization and tensor products of Fock and Bergman spaces, Indiana Univ. Math. J. 43 (1994), 551-582.
    • (1994) Indiana Univ. Math. J. , vol.43 , pp. 551-582
    • Ørsted, B.1    Zhang, G.2
  • 29
    • 0000083829 scopus 로고
    • A weighted Plancherel formula III. The case of a hyperbolic matrix domain
    • J. Peetre and G. Zhang, A weighted Plancherel formula III. The case of a hyperbolic matrix domain, Collect. Math. 43 (1992), 273-301.
    • (1992) Collect. Math. , vol.43 , pp. 273-301
    • Peetre, J.1    Zhang, G.2
  • 30
    • 0002851961 scopus 로고
    • Die Randwerte holomorpher Funktionen auf hermitesch symmetrischen Räumen
    • W. Schmid, Die Randwerte holomorpher Funktionen auf hermitesch symmetrischen Räumen, Invent. Math. 9 (1969), 61-80.
    • (1969) Invent. Math. , vol.9 , pp. 61-80
    • Schmid, W.1
  • 31
    • 0011935698 scopus 로고
    • Une application des opérateurs de Dunkl an théoréme de restriction de Chevalley
    • C. Torossian, Une application des opérateurs de Dunkl an théoréme de restriction de Chevalley, C. R. Acad. Sci. Paris Sér. I Math. 318 (1994), 895-898.
    • (1994) C. R. Acad. Sci. Paris Sér. I. Math. , vol.318 , pp. 895-898
    • Torossian, C.1
  • 32
    • 21844523831 scopus 로고
    • The Berezin transform and invariant differential operators
    • A. Unterberger and H. Upmeier, The Berezin transform and invariant differential operators, Comm. Math. Phys. 164 (1994), 563-597.
    • (1994) Comm. Math. Phys. , vol.164 , pp. 563-597
    • Unterberger, A.1    Upmeier, H.2
  • 33
    • 22444454583 scopus 로고    scopus 로고
    • Properties of some family of hypergeometric orthogonal polynomials in several variables
    • J. F. van Diejen, Properties of some family of hypergeometric orthogonal polynomials in several variables, Trans. Amer. Math. Soc. 351 (1999), 233-270.
    • (1999) Trans. Amer. Math. Soc. , vol.351 , pp. 233-270
    • van Diejen, J.F.1
  • 34
    • 0000201634 scopus 로고    scopus 로고
    • Berezin kernels and tube domains
    • G. van Dijk and M. Pevzner, Berezin kernels and tube domains, J. Funct. Anal. 181 (2001), 189-208.
    • (2001) J. Funct. Anal. , vol.181 , pp. 189-208
    • van Dijk, G.1    Pevzner, M.2
  • 35
    • 0011966787 scopus 로고
    • Polynomial differential operators associated with Hermitian symmetric spaces
    • "Representation Theory of Lie Groups and Lie Algebras, Proceedings of Fuji-Kawaguchiko Conference," 1990 (S. Sano, T. Kawazoe, and T. Oshima, Eds.), World Scientific, Singapore
    • N. Wallach, Polynomial differential operators associated with Hermitian symmetric spaces, in "Representation Theory of Lie Groups and Lie Algebras, Proceedings of Fuji-Kawaguchiko Conference," 1990 (S. Sano, T. Kawazoe, and T. Oshima, Eds.), pp. 76-95, World Scientific, Singapore, 1992.
    • (1992) , pp. 76-95
    • Wallach, N.1
  • 36
    • 0012001742 scopus 로고
    • Differential operators and function spaces "Several Complex Variables in China"
    • Contemporary Mathematics, Providence, RI
    • Z. Yan, Differential operators and function spaces, "Several Complex Variables in China," Contemporary Mathematics, Vol. 142, pp. 121-142, Amer. Math. Soc., Providence, RI, 1993.
    • (1993) Amer. Math. Soc. , vol.142 , pp. 121-142
    • Yan, Z.1
  • 37
    • 0002531834 scopus 로고
    • Tensor products of weighted Bergman spaces and invariant Ha-plitz operators
    • G. Zhang, Tensor products of weighted Bergman spaces and invariant Ha-plitz operators, Math. Scand. 71 (1992), 85-95.
    • (1992) Math. Scand. , vol.71 , pp. 85-95
    • Zhang, G.1
  • 38
    • 0012001743 scopus 로고    scopus 로고
    • Invariant differential operators on Hermitian symmetric spaces and their eigenvalues
    • G. Zhang, Invariant differential operators on Hermitian symmetric spaces and their eigenvalues. Israel J. Math. 119 (2000), 157-185.
    • (2000) Israel J. Math. , vol.119 , pp. 157-185
    • Zhang, G.1
  • 39
    • 23044525493 scopus 로고    scopus 로고
    • Berezin transform on real bounded symmetric domains
    • G. Zhang, Berezin transform on real bounded symmetric domains, Trans. Amer. Math. Soc. 353 (2001), 3769-3787.
    • (2001) Trans. Amer. Math. Soc. , vol.353 , pp. 3769-3787
    • Zhang, G.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.