Large Dimension Homomorphism Spaces Between Specht Modules for Symmetric Groups

2011/03/01 by Dodge, Craig J.
#20C20 #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1103.0246

Abstract

Let F be a field of characteristic p. We show that \Hom_FΣn(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.

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