Spherical distributions on Lie groups and vectors
Author:
R. Penney
Journal:
Trans. Amer. Math. Soc. 223 (1976), 367-384
MSC:
Primary 22E45; Secondary 43A90
DOI:
https://doi.org/10.1090/S0002-9947-1976-0457632-5
MathSciNet review:
0457632
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Abstract | References | Similar Articles | Additional Information
Abstract: Given a Lie group G (not necessarily unimodular) and a subgroup K of G (not necessarily compact), it is shown how to associate with every finite-dimensional unitary irreducible representation of K a class of distributions analogous to the class of spherical functions of height
familiar from the unimodular-maximal compact case. The two concepts agree as nearly as possible. A number of familiar theorems are generalized to our situation. As an application we obtain a generalization of the Frobenius reciprocity theorem and of Plancherel's theorem to arbitrary induced representations of Lie groups.
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Additional Information
DOI:
https://doi.org/10.1090/S0002-9947-1976-0457632-5
Keywords:
vector,
intertwining operator,
spherical distribution
Article copyright:
© Copyright 1976
American Mathematical Society