Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Finite- and infinite-dimensional representation of linear semisimple groups

Authors: James Lepowsky and Nolan R. Wallach
Journal: Trans. Amer. Math. Soc. 184 (1973), 223-246
MSC: Primary 22E45
MathSciNet review: 0327978
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Every representation in the nonunitary principal series of a noncompact connected real semisimple linear Lie group G with maximal compact subgroup K is shown to have a K-finite cyclic vector. This is used to give a new proof of Harish-Chandra's theorem that every member of the nonunitary principal series has a (finite) composition series. The methods of proof are based on finite-dimensional G-modules, concerning which some new results are derived. Further related results on infinite-dimensional representations are also obtained.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 22E45

Retrieve articles in all journals with MSC: 22E45

Additional Information

Keywords: Finite-dimensional representation, infinite-dimensional representation, real semisimple linear Lie group, extensions of M-modules, nonunitary principal series, cyclic vectors, complete multiplicity, irreducible representation, composition series, universal enveloping algebra, subquotient theorem, Iwasawa decomposition
Article copyright: © Copyright 1973 American Mathematical Society