Small modules with interesting rank varieties

2022/05/04 by Lim, Kay Jin, Wang, Jialin
#14J25 (Secondary) #20C20(Primary) 20C30 #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2205.01978

Abstract

This paper focuses on the rank varieties for modules over a group algebra \mathbbFE where E is an elementary abelian p-group and p is the characteristic of an algebraically closed field \mathbbF. In the first part, we give a sufficient condition for a Green vertex of an indecomposable module containing an elementary abelian p-group E in terms of the rank variety of the module restricted to E. In the second part, given a homogeneous algebraic variety V , we explore the problem on finding a small module with rank variety V . In particular, we examine the simple module D^(kp-p+1,1^p-1) for the symmetric group \mathfrakS_kp.

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