Brauer's generalized decomposition numbers and universal deformation rings

Abstract

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

28 pages, 18 figures

References in corpus (5)

• Universal deformation rings and dihedral defect groups
• Universal deformation rings and generalized quaternion defect groups
• p-Adic Lifting Problems and Derived Equivalences
• Universal deformation rings and dihedral blocks with two simple modules
• Inverse Problems for deformation rings

Cited by in corpus (2)

• Universal deformation rings and tame blocks
• Universal deformation rings of group representations, with an application of Brauer's generalized decomposition numbers