Lusztig correspondence and the Gan-Gross-Prasad problem

2021/04/29 by Wang, Zhicheng
#FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2104.14473

Abstract

The Gan-Gross-Prasad problem is to describe the restriction of representations of a classical group G to smaller groups H of the same kind. In this paper, we solved the Gan-Gross-Prasad problem over finite fields completely. In previous work \citeLW1,LW2,LW3,Wang, we study the Gan-Gross-Prasad problem for unipotent representations of finite classical groups. The main tools used are the Lusztig correspondence as well as a formula of Reeder \citeR for the pairings of Deligne-Lusztig characters. We give a reduction decomposition of Reeder's formula, and deduce the Gan-Gross-Prasad problem for arbitrary representations from the unipotent representations by Lusztig correspondence.

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