On Bessel integrals for reducible degenerate principal series representations

Research output: Contribution to journalArticle

1 Citation (Scopus)

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

Fingerprint

Series Representation
Friedrich Wilhelm Bessel
Symmetric matrix
Signature
Correspondence
Orbit
Sufficient Conditions
Character

Keywords

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

ASJC Scopus subject areas

  • Analysis

Cite this

On Bessel integrals for reducible degenerate principal series representations. / Miyazaki, Takuya.

In: Journal of Functional Analysis, Vol. 260, No. 9, 01.05.2011, p. 2579-2597.

Research output: Contribution to journalArticle

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