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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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Spherical distributions on Lie groups and $C^{\infty }$ vectors
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by R. Penney PDF
Trans. Amer. Math. Soc. 223 (1976), 367-384 Request permission

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 $\delta$ of K a class of distributions analogous to the class of spherical functions of height $\delta$ 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
  • © Copyright 1976 American Mathematical Society
  • 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