Vol. 14, No. 2, 2020

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Generalized Schur algebras

Alexander Kleshchev and Robert Muth

Vol. 14 (2020), No. 2, 501–544

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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Schur algebras, symmetric groups
Mathematical Subject Classification 2010
Primary: 16G30
Secondary: 20C20
Received: 30 December 2018
Revised: 19 July 2019
Accepted: 24 September 2019
Published: 29 May 2020
Alexander Kleshchev
Department of Mathematics
University of Oregon
Eugene, OR
United States
Robert Muth
Department of Mathematics
Washington & Jefferson College
Washington, PA
United States