A Generalization of Casselman’s Submodule Theorem

  • Alexander Beilinson
  • Joseph Bernstein
Part of the Progress in Mathematics book series (PM, volume 40)


Let G be a real reductive Lie group, g; its Lie algebra. Let M be an irreducible Harish-Chandra module. Using some fine analytic arguments, based on the study of asymptotic behavior of matrix coefficients, Casselman has proved that M can be imbedded into a principal series representation [2,3].


Simple Root Open Dense Subset Flag Variety Invertible Sheaf Principal Series Representation 
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  1. [1]
    A. Beilinson, J.N. Bernstein, Localisation de ℊ-modules, C.R. Acad. Sci. Paris, 292, (1981), 15–18.Google Scholar
  2. [2]
    W. Casselman, Differential equations satisfied by matrix coefficients, preprint.Google Scholar
  3. [3]
    D. Miličić, Notes on asymptotics of admissible representations of semi-simple Lie groups, Institute for Advanced Study, 1976.Google Scholar
  4. [4]
    D. Mumford, Lectures on curves on an algebraic surface, Ann. of Math. Studies, Vol. 59, Princeton University Press, 1966.Google Scholar
  5. [5]
    J.T. Stafford, N.R. Wallach, The restriction of admissible modules to parabolic subalgebras, Trans. Amer. Math. Soc. 272(1982), 333–350.CrossRefGoogle Scholar

Copyright information

© Birkhäuser Boston, Inc. 1983

Authors and Affiliations

  • Alexander Beilinson
  • Joseph Bernstein

There are no affiliations available

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