Restriction of a cuspidal module for finite general linear groups

In this article, we consider two subgroups A and A′ of GLn(q) containing a fixed unipotent subgroup U, either of which may be identified with the group of all affine transformations of an n−1 dimensional affine space. We describe the restriction of an irreducible cuspidal module to the subgroup A∩A′ of GLn(q) and prove that it is multiplicity-free.