SPECHT MODULES AND SIMPLE MODULES FOR CENTRALIZER ALGEBRAS OF THE SYMMETRIC GROUP

Let Sigma(n) be the symmetric group on n letters. For l <= n identify Sigma(l) with a subgroup of Sigma(n) in the natural way. Let k be an algebraically closed field of characteristic p. This article begins to develop a theory for modules over the centralizer algebras k Sigma(n)Sigma(l) that is analogous to James's theory of permutation modules, Specht modules, and simple modules over k Sigma(n). We make a conjecture about how to construct all simple k Sigma(n)Sigma(l) - modules, we develop tools to test the conjecture, and we prove that it is correct for all n when l < p.