Relative discrete series of line bundles over bounded symmetric domains

Annales de l'Institut Fourier

Volumn 46, Issue 4, 1996, Pages 1011-1026

  Dooley, A H ^a   Orsted B ^b   Zhang, G ^a  

^a UNIVERSITY OF NEW SOUTH WALES   (Australia)

^b UNIVERSITY OF SOUTHERN DENMARK   (Denmark)

Author keywords

Bounded symmetric domain; Holomorphic discrete series; Line bundle; Relative discrete series

Indexed keywords

EID: 0030502089     PISSN: 03730956     EISSN: None     Source Type: Journal    
DOI: 10.5802/aif.1538     Document Type: Article

References (22)

1. W. CASSELMAN & D. MILIĆIC̀, Asymptotic behaviour of matrix coefficients of admissible representations, Duke Math. J., 49 (1982), 869-930.
2. J. FARAUT & A. KORANYI, Function spaces and reproducing kernels on bounded symmetric domains, J. Funct. Anal., 89 (1990), 64-89.
3. HARISH-CHANDRA, Representations of semisimple Lie groups IV, Amer. J. Math., 77 (1955), 743-777.
4. S. HELGASON, Groups and geometric analysis, Academic Press, London, 1984.
5. S. JANSON & J. PEETRE, A new generalization of Hankel operators, Math. Nachr., 132 (1987), 313-328.
6. K. D. JOHNSON, On a ring of invariant polynomials on a Hermitian symmetric space, J. of Algebra, 67 (1980), 72-81.
7. H. LIU & L. PENG, Weighted Plancherel formula. Irreducible unitary representations and eigenspace representations, Math. Scand., 72 (1993), 99-119.
8. O. LOOS, Bounded Symmetric Domains and Jordan Pairs, University of California, Irvine, 1977.
9. B. ØRSTED & G. ZHANG, Tensor products of analytic continuations of holomorphic discrete series, preprint, 1994.
10. B. ØRSTED & G. ZHANG, in preparation.
11. J. PEETRE, Covariant Laplaceans and Cauchy-Riemann operators for a Cartan domain, manuscript.
12. J. PEETRE, L. PENG & G. ZHANG, A weighted Plancherel formula I. The case of the unit disk. Application to Hankel operators, technical report, Stockholm, 1990.
13. J. PEETRE & G. ZHANG, A weighted Plancherel formula III. The case of a hyperbolic matrix ball, Collect. Math., 43 (1992), 273-301.
14. J. REPKA, Tensor products of holomorphic discrete series, Can. J. Math., 31 (1979), 836-844.
15. I. SATAKE, Algebraic structures of symmetric domains, Iwanami Shoten and Princeton Univ. Press, Tokyo and Princeton, NJ, 1980.
16. H. SCHLICHTKRULL, One-dimensional K-types in finite dimensional representations of semisimple Lie groups: A generalization of Helgason's theorem, Math. Scand., 54 (1984), 279-294.
17. N. SHIMENO, The Plancherel formula for spherical functions with one-dimensional K-type on a simply connected simple Lie group of Hermitian type, J. Funct. Anal., 121 (1994), 331-388.
18. H. UPMEIER, Jordan algebras and harmonic analysis on symmetric spaces, Amer. J. Math., 108 (1986), 1-25.
19. N. WALLACH, The analytic continuation of the discrete series. I, II, Trans. Amer. Math. Soc., 251 (1979), 1-17; 19-37.
20. D. P. ZELOBENKO, Compact Lie groups and their representations, Amer. Math. Soc., Transl. Math. Monographs, vol. 40, Providence, Rhode Island, 1973.
21. G. ZHANG, Ha-plitz operators between Moebius invariant subspaces, Math. Scand., 71 (1992), 69-84.
22. G. ZHANG, A weighted Plancherel formula II. The case of the ball, Studia Math., 102 (1992), 103-120.