On the Gan-Gross-Prasad problem for finite classical groups

TL;DR

This paper investigates the Gan-Gross-Prasad problem for finite classical groups, providing explicit branching laws for unipotent representations and a reduction formula for arbitrary representations.

Contribution

It offers complete solutions for unipotent representations and introduces a reduction approach for the general Gan-Gross-Prasad problem in finite classical groups.

Findings

Complete answers for unipotent representations

Explicit branching laws derived

Reduction formula for arbitrary representations

Abstract

In this paper we study the Gan-Gross-Prasad problem for finite classical groups. Our results provide complete answers for unipotent representations, and we obtain the explicit branching laws for these representations. Moreover, for arbitrary representations, we give a formula to reduce the Gan-Gross-Prasad problem to the restriction problem of Deligne-Lusztig characters.