On Bessel integrals for reducible degenerate principal series representations

Takuya Miyazaki

doi:10.1016/j.jfa.2011.01.013

On Bessel integrals for reducible degenerate principal series representations

Takuya Miyazaki

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

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 GL_n(R)-orbits in the set of real symmetric matrices of size n and irreducible submodules of the reducible principal series representations.

Original language	English
Pages (from-to)	2579-2597
Number of pages	19
Journal	Journal of Functional Analysis
Volume	260
Issue number	9
DOIs	https://doi.org/10.1016/j.jfa.2011.01.013
Publication status	Published - 2011 May 1

Keywords

Degenerate principal series representations
Generalized Bessel integrals
Generalized confluent hypergeometric functions

ASJC Scopus subject areas

Analysis

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10.1016/j.jfa.2011.01.013

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AB - 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.

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KW - Generalized Bessel integrals

KW - Generalized confluent hypergeometric functions

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On Bessel integrals for reducible degenerate principal series representations

Abstract

Keywords

ASJC Scopus subject areas

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