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The local structure of characters

Authors
Journal
Journal of Functional Analysis
0022-1236
Publisher
Elsevier
Publication Date
Volume
37
Issue
1
Identifiers
DOI: 10.1016/0022-1236(80)90026-9
Disciplines
  • Mathematics

Abstract

Abstract Let G be a connected real semisimple Lie group with Lie algebra g. Let g = t̆ + s be the Cartan decomposition and K the maximal compact subgroup with Lie algebra t̆. Let Θ be the character of an irreducible representation. Then Θ has an asymptotic expansion at zero (in the sense of Taylor series). As consequences of this expansion we obtain results about the asymptotic directions in which the K-types occur and about the Gelfand-Kirillov dimension of the representation.

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