Decomposing tensor products and exterior and symmetric squares

Abstract

We describe a new algorithm for decomposing tensor products of indecomposable KG-modules into a direct sum of indecomposable KG-modules when K is a field of finite characteristic p and G a cyclic group of order q = pt . We use this algorithm to extend reciprocity results of Gow and Laffey relating the exterior and symmetric squares of indecomposable modules when p is odd.