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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Harish-Chandra modules with the unique embedding property


Author: David H. Collingwood
Journal: Trans. Amer. Math. Soc. 281 (1984), 1-48
MSC: Primary 22E45; Secondary 20G05, 22E47
MathSciNet review: 719657
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Abstract: Let $ G$ be a connected semisimple real matrix group. In view of Casselman's subrepresentation theorem, every irreducible admissible representation of $ G$ may be realized as a submodule of some principal series representation. We give a classification of representations with a unique embedding into principal series, in the case of regular infinitesimal character. Our basic philosophy is to link the theory of asymptotic behavior of matrix coefficients with the theory of coherent continuation of characters. This is accomplished by using the "Jacquet functor" and the Kazhdan-Lusztig conjectures.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1984-0719657-6
PII: S 0002-9947(1984)0719657-6
Keywords: Representations of semisimple Lie groups, embedding theorems, asymptotic behavior of matrix coefficients, coherent continuation, composition series problem, Kazhdan-Lusztig conjectures
Article copyright: © Copyright 1984 American Mathematical Society