Generalized Preservation Principle in Finite Theta Correspondence

TL;DR

This paper extends the preservation principle in Howe correspondences from cuspidal characters to all irreducible characters of classical groups, broadening its applicability in representation theory.

Contribution

It generalizes the preservation principle to all irreducible characters of classical groups, beyond cuspidal characters, in the context of finite reductive dual pairs.

Findings

Preservation principle now applies to all irreducible characters of classical groups.

Broadens understanding of Howe correspondences in finite reductive dual pairs.

Enhances the theoretical framework of representation theory for classical groups.

Abstract

It is known that irreducible cuspidal characters satisfy the preservation principle in the Howe correspondences of finite reductive dual pairs. In this article, we generalize the preservation principle to any irreducible characters of classical groups.