The Benson-Symonds Invariant for Permutation Modules

2020/12/01 by Upadhyay, Aparna · 1 citation
#05E10 #20C20 #20C30 #Combinatorics (math.CO) #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2012.00341

Abstract

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 permutation modules of the symmetric group corresponding to two-part partitions 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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• The Benson -- Symonds Invariant for Ordinary and Signed Permutation Modules
• Butler's Method applied to ℤ_p[C_p× C_p]-permutation modules
• Permutation dimensions of prime cyclic groups
• Symmetric Powers
• The source permutation module of a block of a finite group algebra