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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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On the discrete series of generalized Stiefel manifolds
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Trans. Amer. Math. Soc. 340 (1993), 753-766 Request permission

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
  • J. D. Adams, Discrete spectrum of the reductive dual pair $(\textrm {O}(p,\,q),\,\textrm {Sp}(2m))$, Invent. Math. 74 (1983), no. 3, 449–475. MR 724015, DOI 10.1007/BF01394246
  • Nguyen Huu Anh, Restriction of the principal series of $\textrm {SL}(n,\,\textbf {C})$ to some reductive subgroups, Pacific J. Math. 38 (1971), 295–314. MR 327980
  • Dan Barbasch and David A. Vogan Jr., The local structure of characters, J. Functional Analysis 37 (1980), no. 1, 27–55. MR 576644, DOI 10.1016/0022-1236(80)90026-9
  • Dan Barbasch and David Vogan, Primitive ideals and orbital integrals in complex classical groups, Math. Ann. 259 (1982), no. 2, 153–199. MR 656661, DOI 10.1007/BF01457308
  • M. Cowling, U. Haagerup, and R. Howe, Almost $L^2$ matrix coefficients, J. Reine Angew. Math. 387 (1988), 97–110. MR 946351
  • Jacques Dixmier, Les $C^{\ast }$-algèbres et leurs représentations, Cahiers Scientifiques, Fasc. XXIX, Gauthier-Villars & Cie, Éditeur-Imprimeur, Paris, 1964 (French). MR 0171173
  • Stephen Gelbart, Holomorphic discrete series for the real symplectic group, Invent. Math. 19 (1973), 49–58. MR 320231, DOI 10.1007/BF01418850
  • R. Howe, $\theta$-series and invariant theory, Automorphic forms, representations and $L$-functions (Proc. Sympos. Pure Math., Oregon State Univ., Corvallis, Ore., 1977) Proc. Sympos. Pure Math., XXXIII, Amer. Math. Soc., Providence, R.I., 1979, pp. 275–285. MR 546602
  • Roger Howe, Transcending classical invariant theory, J. Amer. Math. Soc. 2 (1989), no. 3, 535–552. MR 985172, DOI 10.1090/S0894-0347-1989-0985172-6
  • —, On a notion of rank for unitary representations of classical groups, C.I.M.E Summer School on Harmonic Analysis, Cortona, 1980.
  • Roger Howe, Wave front sets of representations of Lie groups, Automorphic forms, representation theory and arithmetic (Bombay, 1979), Tata Inst. Fund. Res. Studies in Math., vol. 10, Tata Institute of Fundamental Research, Bombay, 1981, pp. 117–140. MR 633659
  • Toshiyuki Kobayashi, Singular unitary representations and discrete series for indefinite Stiefel manifolds $\textrm {U}(p,q;\textbf {F})/\textrm {U}(p-m,q;\textbf {F})$, Mem. Amer. Math. Soc. 95 (1992), no. 462, vi+106. MR 1098380, DOI 10.1090/memo/0462
  • Jian-Shu Li, Singular unitary representations of classical groups, Invent. Math. 97 (1989), no. 2, 237–255. MR 1001840, DOI 10.1007/BF01389041
  • —, Theta lifting for unitary representations with non-zero cohomology, Duke Math. J. (3) 61 (1990).
  • Toshio Ōshima and Toshihiko Matsuki, A description of discrete series for semisimple symmetric spaces, Group representations and systems of differential equations (Tokyo, 1982) Adv. Stud. Pure Math., vol. 4, North-Holland, Amsterdam, 1984, pp. 331–390. MR 810636, DOI 10.2969/aspm/00410331
  • C. Moeglin, Correspondance de Howe pour les paires reductive duales, quelques calculs dans le cas Archimedien, preprint.
  • Stephen Rallis and Gérard Schiffmann, Weil representation. I. Intertwining distributions and discrete spectrum, Mem. Amer. Math. Soc. 25 (1980), no. 231, iii+203. MR 567800, DOI 10.1090/memo/0231
  • Henrik Schlichtkrull, A series of unitary irreducible representations induced from a symmetric subgroup of a semisimple Lie group, Invent. Math. 68 (1982), no. 3, 497–516. MR 669427, DOI 10.1007/BF01389414
  • David A. Vogan Jr., Unitary representations of reductive Lie groups, Annals of Mathematics Studies, vol. 118, Princeton University Press, Princeton, NJ, 1987. MR 908078
  • —, Irreducibility of discrete series representations for semi-simple symmetric spaces, Adv. Stud. Pure Math., no. 14, Academic Press, 1988, pp. 191-221.
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Additional Information
  • © Copyright 1993 American Mathematical Society
  • 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