Projective modules for the symmetric group and Young's seminormal form

Abstract

Projective modules for the symmetric group and Young's seminormal form.steen ryom-hansen *We study the representation theory of the symmetric group Sn in positive characteristic p. Using features of the LLT-algorithm we give a conjectural description of the projective cover P (λ) of the simple module D(λ) where λ is a p-restricted partition such that all ladders of the corresponding ladder partition are of order less than p. Inspired by the recent theory of KLRalgebras, we explain an algorithm that allows us to verify this conjectural description for n ≤ 15, at least.