Generalized Schur algebras

Kleshchev, Alexander; Muth, Robert

doi:10.2140/ant.2020.14.501

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Generalized Schur algebras

Alexander Kleshchev and Robert Muth

Vol. 14 (2020), No. 2, 501–544

DOI: 10.2140/ant.2020.14.501

Abstract

We define and study a new class of bialgebras, which generalize certain Turner double algebras related to generic blocks of symmetric groups. Bases and generators of these algebras are given. We investigate when the algebras are symmetric which is relevant to block theory of finite groups. We then establish a double centralizer property related to blocks of Schur algebras.

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Keywords

Schur algebras, symmetric groups

Mathematical Subject Classification 2010

Primary: 16G30

Secondary: 20C20

Milestones

Received: 30 December 2018

Revised: 19 July 2019

Accepted: 24 September 2019

Published: 29 May 2020

Authors

Alexander Kleshchev
Department of Mathematics University of Oregon Eugene, OR United States

Robert Muth
Department of Mathematics Washington & Jefferson College Washington, PA United States

Vol. 14, No. 2, 2020