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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 2024 MCQ for Transactions of the American Mathematical Society is 1.48 .

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On the character of Weil’s representation
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by Roger E. Howe
Trans. Amer. Math. Soc. 177 (1973), 287-298
DOI: https://doi.org/10.1090/S0002-9947-1973-0316633-5

Abstract:

The importance of certain representations of symplectic groups, usually called Weil representations, for the general problem of finding representations of certain group extensions is made explicit. Some properties of the character of Weil’s representation for a finite symplectic group are given and discussed, again in the context of finding representations of group extensions. As a by-product, the structure of anisotropic tori in symplectic groups is given.
References
  • L. Auslander and B. Kostant, Polarization and unitary representations of solvable Lie groups, Invent. Math. 14 (1971), 255–354. MR 293012, DOI 10.1007/BF01389744
  • Charles W. Curtis and Irving Reiner, Representation theory of finite groups and associative algebras, Pure and Applied Mathematics, Vol. XI, Interscience Publishers (a division of John Wiley & Sons, Inc.), New York-London, 1962. MR 0144979
  • H. Jacquet and R. P. Langlands, Automorphic forms on $\textrm {GL}(2)$, Lecture Notes in Mathematics, Vol. 114, Springer-Verlag, Berlin-New York, 1970. MR 0401654, DOI 10.1007/BFb0058988
  • A. A. Kirillov, Unitary representations of nilpotent Lie groups, Uspehi Mat. Nauk 17 (1962), no. 4 (106), 57–110 (Russian). MR 0142001
  • Calvin C. Moore, Group extensions of $p$-adic and adelic linear groups, Inst. Hautes Études Sci. Publ. Math. 35 (1968), 157–222. MR 244258
  • J. Shalika, Representation theory of the 2x2 unimodular group over local fields, Notes, Institute for Advanced Study, Princeton, N. J., 1966.
  • André Weil, Sur certains groupes d’opérateurs unitaires, Acta Math. 111 (1964), 143–211 (French). MR 165033, DOI 10.1007/BF02391012
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Bibliographic Information
  • © Copyright 1973 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 177 (1973), 287-298
  • MSC: Primary 22E50; Secondary 20G05, 20G25, 22E70
  • DOI: https://doi.org/10.1090/S0002-9947-1973-0316633-5
  • MathSciNet review: 0316633