  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 \cite{LW1,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 \cite{R} 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.

Representation Theory