On the dimension of some modular irreducible representations of the symmetric group

Abstract

We compute the dimension of some irreducible representations of the symmetric groups in characteristic p (Theorem 2). The representations considered here are associated with Young diagrams m: m1≥m2≥...≥mlsuch that m1−ml≤(p−l). The formula is based on a variant of Verlinde's formula which computes some tensor product multiplicities of indecomposable modules for GL1(F p ).