Large dimension homomorphism spaces between Specht modules for symmetric groups

Abstract

Let F be a field of characteristic p . We show that Hom F Σ n ( S λ , S μ ) can have arbitrarily large dimension as n and p grow, where S λ and S μ are Specht modules for the symmetric group Σ n . Similar results hold for the Weyl modules of the general linear group. Every previously computed example has been at most one-dimensional, with the exception of Specht modules over a field of characteristic two. The proof uses the work of Chuang and Tan, providing detailed information about the radical series of Weyl modules in Rouquier blocks.