A LITTLEWOOD-RICHARDSON FILTRATION AT ROOTS OF 1 FOR QUANTUM DEFORMATIONS OF SKEW SCHUR MODULES

Abstract

It is well known that the classical skew Schur module is isomorphic to a direct sum of (non-skew) Schur modules, the multiplicities being given by the Littlewood-Richardson rule. We define a multiparameter quantum deformation of the classical skew Schur module, and show that up to a filtration, it still has a Littlewood-Richardson decomposition. The ground ring can be any commutative ring, and q is allowed to be a root of 1.