Brauer’s generalized decomposition numbers and universal deformation rings

Abstract

The versal deformation ring R ( G , V ) R(G,V) of a mod p p representation V V of a profinite group G G encodes all isomorphism classes of lifts of V V to representations of G G over complete local commutative Noetherian rings. We introduce a new technique for determining R ( G , V ) R(G,V) when G G is finite which involves Brauer’s generalized decomposition numbers.