Ennola duality for decomposition of tensor products

Abstract

The aim of this paper is to investigate Ennola duality for decomposition of tensor products of irreducible characters of finite general linear groups and finite unitary groups. We prove that Ennola duality holds generically and give a geometric interpretation using the cohomology of quiver varieties. For non-generic characters (like unipotent characters), Ennola duality does not work just by replacing q by -q. We construct two-variable polynomials that interpolate multiplicities for finite general linear groups and finite unitary groups in the unipotent case (which can be considered as Ennola duality).