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.
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References
A. Beilinson, J.N. Bernstein, Localisation de ℊ-modules, C.R. Acad. Sci. Paris, 292, (1981), 15–18.
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J.T. Stafford, N.R. Wallach, The restriction of admissible modules to parabolic subalgebras, Trans. Amer. Math. Soc. 272(1982), 333–350.
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© 1983 Birkhäuser Boston, Inc.
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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
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DOI: https://doi.org/10.1007/978-1-4684-6730-7_3
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