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

2013/03/24 by Ryom-Hansen, Steen
#FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1303.5969

Abstract

We study the representation theory of the symmetric group S_n 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.

Related

• Young Modules and Schur algebras
• Young's seminormal form and simple modules for S_n in characteristic p
• The non-projective part of the Lie module for the symmetric group
• The Howe duality and the Projective Representations of Symmetric Groups
• "Frobenius twists" in the representation theory of the symmetric group