English

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

Representation Theory 2021-01-27 v1 Combinatorics Group Theory

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 γG(M)\gamma_G(M) for a finite dimensional module MM of a finite group GG 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.

Keywords

Cite

@article{arxiv.2101.10612,
  title  = {The Benson -- Symonds Invariant for Ordinary and Signed Permutation Modules},
  author = {Aparna Upadhyay},
  journal= {arXiv preprint arXiv:2101.10612},
  year   = {2021}
}

Comments

14 pages. arXiv admin note: substantial text overlap with arXiv:2012.00341

R2 v1 2026-06-23T22:32:00.223Z