Universal deformation rings and fusion
Representation Theory
2014-07-03 v3
Abstract
Let p be a prime, M be a finite group, F be the field with p elements, and V be an absolutely irreducible FM-module. Then V has a universal deformation ring R(M,V) whose structure is closely related to the first and second cohomology groups of M with coefficients in Hom_F(V,V). We consider the case when M is an extension of a dihedral group G whose order is relatively prime to p by an elementary abelian p-group N of rank 2. We determine the cohomology groups and also R(M,V) for various V and show to what extent R(M,V) sees the fusion of N in M.
Cite
@article{arxiv.1305.3012,
title = {Universal deformation rings and fusion},
author = {David C. Meyer},
journal= {arXiv preprint arXiv:1305.3012},
year = {2014}
}