On Ext-Quivers of Blocks of Weight Two for Symmetric Groups

2020/08/25 by Danz, Susanne, Erdmann, Karin · 1 citation
#16D90 (secondary) #20C30 (primary) #29C20 #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2008.10999

Abstract

In this paper we investigate blocks of symmetric groups of weight 2 over fields of odd characteristic p. We develop an algorithm that relates the quivers of two such blocks forming a (2:1) pair, as introduced by Scopes. We then apply the algorithm to blocks whose p-cores are hook partitions, in order to explicitly determine the quivers of these blocks. As a consequence we conclude that two p-blocks B₁ and B₂ of symmetric groups of weight 2 whose p-cores are hook partitions are Morita equivalent if and only if B₂ or its conjugate block is in the same Scopes class as B₁.

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• Homological dimensions of Schur algebras S(p,2p) and an Auslander-type correspondence

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