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

الأصل · EN

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 Khovanov-Lauda-Rouquier algebras we explain an algorithm that allows us to verify this conjectural description for n ≤ 15, at least.