The Benson -- Symonds Invariant for Ordinary and Signed Permutation Modules

2021/01/26 by Upadhyay, Aparna · 1 citation
#20C20 #Combinatorics (math.CO) #FOS: Mathematics #Group Theory (math.GR) #Primary 20C30 #Representation Theory (math.RT) #Secondary 05E10

paper · doi:10.48550/arxiv.2101.10612

Abstract

The signed permutation modules are a simultaneous generalization of the ordinary permutation modules and the twisted permutation modules of the symmetric group. In a recent paper Dave Benson and Peter Symonds defined a new invariant γ_G(M) for a finite dimensional module M of a finite group G which attempts to quantify how close a module is to being projective. In this paper, we determine this invariant for all the signed permutation modules of the symmetric group using tools from representation theory and combinatorics.

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• Non-negligible summands in tensor powers of some modular representations of finite p-groups

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