On signed p-Kostka matrices

Abstract

We show that the signed p-Kostka numbers depend just on p-Kostka numbers and the multiplicities of projective indecomposable modules in certain signed Young permutation modules. We then examine the signed p-Kostka number k₍α|ᵦ₎,₍λ|pμ₎ in the case when |β|=p|μ|. This allows us to explicitly describe the multiplicities of direct summands of a signed Young permutation module lying in the principal block of F𝕾ᵐᵖ in terms of the p-Kostka numbers.