Abstract
Let Gℝ be a real reductive Lie group, g;ℝ 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].
The second author was supported by the National Science Foundation.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
A. Beilinson, J.N. Bernstein, Localisation de ℊ-modules, C.R. Acad. Sci. Paris, 292, (1981), 15–18.
W. Casselman, Differential equations satisfied by matrix coefficients, preprint.
D. Miličić, Notes on asymptotics of admissible representations of semi-simple Lie groups, Institute for Advanced Study, 1976.
D. Mumford, Lectures on curves on an algebraic surface, Ann. of Math. Studies, Vol. 59, Princeton University Press, 1966.
J.T. Stafford, N.R. Wallach, The restriction of admissible modules to parabolic subalgebras, Trans. Amer. Math. Soc. 272(1982), 333–350.
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1983 Birkhäuser Boston, Inc.
About this chapter
Cite this chapter
Beilinson, A., Bernstein, J. (1983). A Generalization of Casselman’s Submodule Theorem. In: Trombi, P.C. (eds) Representation Theory of Reductive Groups. Progress in Mathematics, vol 40. Birkhäuser Boston. https://doi.org/10.1007/978-1-4684-6730-7_3
Download citation
DOI: https://doi.org/10.1007/978-1-4684-6730-7_3
Publisher Name: Birkhäuser Boston
Print ISBN: 978-0-8176-3135-2
Online ISBN: 978-1-4684-6730-7
eBook Packages: Springer Book Archive