Universal deformation rings and fusion

2013/05/14 by David C. Meyer, Meyer, David C.
Mathematics · #FOS: Mathematics #Representation Theory (math.RT) #math.RT

paper · pdf · doi:10.48550/arxiv.1305.3012

arxiv created 2014/07/02 · arxiv updated 2014/07/03

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.

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