On Bessel integrals for reducible degenerate principal series representations

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Abstract

We discuss generalized Bessel integrals with nondegenerate characters, which are assigned to irreducible submodules of a reducible degenerate principal series representation of Sp(n,R). Then we give sufficient conditions for their vanishings which are based on the signatures of the nondegenerate characters. This consequently suggests a reasonable correspondence between open GLn(R)-orbits in the set of real symmetric matrices of size n and irreducible submodules of the reducible principal series representations.

Original languageEnglish
Pages (from-to)2579-2597
Number of pages19
JournalJournal of Functional Analysis
Volume260
Issue number9
DOIs
Publication statusPublished - 2011 May 1

Keywords

  • Degenerate principal series representations
  • Generalized Bessel integrals
  • Generalized confluent hypergeometric functions

ASJC Scopus subject areas

  • Analysis

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