Decomposition of the Uniform Projection of the Weil Character

TL;DR

This paper derives a decomposition formula for the uniform projection of the Weil character in finite reductive dual pairs, advancing the understanding of the Howe correspondence on unipotent characters.

Contribution

It provides the first explicit decomposition formula for the uniform projection of the Weil character in symplectic-orthogonal dual pairs, confirming a key conjecture.

Findings

Decomposition formula for the Weil character's uniform projection

Explicit description of the Howe correspondence on unipotent characters

Confirmation of Aubert-Michel-Rouquier conjecture

Abstract

In this paper we obtain a decomposition formula of the uniform projection of the Weil character of a finite reductive dual pair consisting of a symplectic group and an even orthogonal group. This is the first and major step to give an explicit description of the Howe correspondence on unipotent characters confirming a conjecture by Aubert-Michel-Rouquier.