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

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: m₁m₂...m_lsuch that m₁–m_l(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).