Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

On the discrete series of generalized Stiefel manifolds


Author: Jian-Shu Li
Journal: Trans. Amer. Math. Soc. 340 (1993), 753-766
MSC: Primary 22E46; Secondary 22E45
DOI: https://doi.org/10.1090/S0002-9947-1993-1127156-0
MathSciNet review: 1127156
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: A study of the discrete series of generalized Stiefel manifolds is made using the oscillator representation. New infinite families of such discrete series are constructed.


References [Enhancements On Off] (What's this?)

  • [1] J. Adams, Discrete spectrum of the reductive dual pair $ (O(p,q),Sp(2m))$, Invent. Math. 74 (1983), 449-475. MR 724015 (85k:22031)
  • [2] H. Anh, Restriction of the principal series of $ SL(n,{\mathbf{C}})$ to some reductive subgroups, Pacific J. Math. 38 (1971), 295-313. MR 0327980 (48:6322)
  • [3] D. Barbasch and D. Vogan Jr., The local structure of characters, J. Funct. Anal. 37 (1980), 27-55. MR 576644 (82e:22024)
  • [4] -, Primitive ideals and orbital integrals in complex classical groups, Math. Ann. 259 (1982), 153-199. MR 656661 (83m:22026)
  • [5] M. Cowling, U. Haagerup, and R. Howe, Almost $ {L^2}$ matrix coefficients, J. Reine Angew. Math. 387 (1988), 97-110. MR 946351 (89i:22008)
  • [6] J. Diximir, Les $ {{\mathbf{C}}^\ast}$-algebres et leurs representations, Gauther-Villars, Paris, 1964. MR 0171173 (30:1404)
  • [7] S. Gelbart, Holomorphic discrete series for the real symplectic group, Invent. Math. 19 (1973), 19-58. MR 0320231 (47:8770)
  • [8] R. Howe, Theta series and invariant theory, Proc. Sympos. Pure Math., vol. 33, Amer. Math. Soc., Providence, R.I., 1979. MR 546602 (81f:22034)
  • [9] -, Transcending classical invariant theory, J. Amer. Math. Soc. (3) 2 (1989), 535-552. MR 985172 (90k:22016)
  • [10] -, On a notion of rank for unitary representations of classical groups, C.I.M.E Summer School on Harmonic Analysis, Cortona, 1980.
  • [11] -, Wave front sets of representations of Lie groups, automorphic forms, representation theory, and arithmetic, Papers presented at the Bombay Colloquium, 1979, Tata Institute of Fundamental Research, Bombay, 1981, pp. 117-140. MR 633659 (83c:22014)
  • [12] T. Kobayashi, Singular unitary representations and discrete series for indefinite Stiefel manifolds $ U(p,q;{\mathbf{F}})/U(p - m,q;{\mathbf{F}})$, preprint. MR 1098380 (92f:22023)
  • [13] J. S. Li, Singular unitary representations of classical groups, Invent. Math. 97 (1989), 237-255. MR 1001840 (90h:22021)
  • [14] -, Theta lifting for unitary representations with non-zero cohomology, Duke Math. J. (3) 61 (1990).
  • [15] T. Matsuki and T. Oshima, A description of discrete series for semi-simple symmetric spaces, Adv. Stud. Pure Math., no. 4, Academic Press, 1984, pp. 331-390. MR 810636 (87m:22042)
  • [16] C. Moeglin, Correspondance de Howe pour les paires reductive duales, quelques calculs dans le cas Archimedien, preprint.
  • [17] S. Rallis and G. Schiffmann, Weil representation. I. Intertwining distributions and discrete spectrum, Mem. Amer. Math. Soc., vol. 25, no. 231, 1980. MR 567800 (81j:22007)
  • [18] H. Schlichtkrull, A series of unitary irreducible representations induced from a symmetric subgroup of a semi-simple Lie group, Invent. Math. 68 (1982), 497-516. MR 669427 (84d:22027)
  • [19] D. Vogan, Unitary representations of real reductive groups, Ann. of Math. Studies, vol. 118, Princeton Univ. Press, Princeton, N.J, 1987. MR 908078 (89g:22024)
  • [20] -, Irreducibility of discrete series representations for semi-simple symmetric spaces, Adv. Stud. Pure Math., no. 14, Academic Press, 1988, pp. 191-221.

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 22E46, 22E45

Retrieve articles in all journals with MSC: 22E46, 22E45


Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1993-1127156-0
Article copyright: © Copyright 1993 American Mathematical Society

American Mathematical Society