Homomorphisms from specht modules to signed young permutation modules

Abstract

© 2018, Institute of Mathematics. All rights reserved. We construct a class ΘR of homomorphisms from a Specht module (formula presented) to a signed permutation module Mℤ(α|β) which generalises James's construction of homomorphisms whose codomain is a Young permutation module. We show that any ϕ ∈ Homℤϭn (formula presented) lies in the -span of Θsstd, a subset of ΘR corresponding to semistandard λ-tableaux of type (α|β). We also study the conditions for which (formula presented) - a subset of HomFϭn (formula presented) induced by Θsstd - is linearly independent, and show that it is a basis for HomFϭn (formula presented) when Fϭn is semisimple.