On the inverse problem for deformations of finite group representations

2019/10/27 by Marcin Lara, Lara, Marcin
Mathematics · #20C05 #20C11 #20C20 #Advanced Algebra and Geometry #FOS: Mathematics #Finite Group Theory Research #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology #Number Theory (math.NT) #Representation Theory (math.RT) #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.1910.12160

openalex publication_date 2019/10/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let s be even and q=p^s. We show that the ring W(\mathbbF_q)[ [X] ]/(X²-pX) is a quotient of the universal deformation ring of a representation of a finite group. This amounts to giving an example of a finite group and its \mathbbF_q-representation that lifts to W(\mathbbF_q) in two different ways and satisfies certain subtle extra conditions. We achieve this by studying representations of SL(2,\mathbbF_p²).

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