Bessel Models for General Admissible Induced Representations: The Compact Stabilizer Case

TL;DR

This paper studies Bessel models for admissible induced representations with compact stabilizer, providing a comprehensive analysis of Jacquet integrals, their holomorphic continuation, and explicit examples in the context of parabolic subgroups with abelian nilradical.

Contribution

It offers a complete description of Bessel models for generic characters with compact stabilizer, extending the understanding of Jacquet integrals and induced representations in this setting.

Findings

Holomorphic continuation of Jacquet integrals established

Complete classification of Bessel models for compact stabilizer cases

Explicit examples illustrating the theoretical results

Abstract

A holomorphic continuation of Jacquet type integrals for parabolic subgroups with abelian nilradical is studied. Complete results are given for generic characters with compact stabilizer and arbitrary representations induced from admissible representations. A description of all of the pertinent examples is given. These results give a complete description of the Bessel models corresponding to compact stabilizer.