On Ext-quivers of blocks of weight two for symmetric groups

JOURNAL OF PURE AND APPLIED ALGEBRA

卷:226

Article

Danz, Susanne¹  Erdmann, Karin² 

[1] Katholische Univ Eichstatt Ingolstadt, FB Math, D-85072 Eichstatt, Germany

[2] Univ Oxford, Math Inst, Oxford OX2 6GG, England

关键词: Symmetric group;    Ext-quiver;    Specht module;    Hook partition;    Morita equivalence;   

DOI  :  10.1016/j.jpaa.2021.106817

来源: Elsevier

【 摘 要 】

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 B-1 and B-2 of symmetric groups of weight 2 whose p-cores are hook partitions are Morita equivalent if and only if B-2 or its conjugate block is in the same Scopes class as B-1. (C) 2021 Elsevier B.V. All rights reserved.

【 授权许可】

Free