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Schur algebras of Brauer algebras I

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Abstract

Schur algebras of Brauer algebras are defined as endomorphism algebras of certain direct sums of ‘permutation modules’ over Brauer algebras. Explicit combinatorial bases of these new Schur algebras are given; in particular, these Schur algebras are defined integrally. The new Schur algebras are related to the Brauer algebra by Schur–Weyl dualities on the above sums of permutation modules. Moreover, they are shown to be quasi-hereditary. Over fields of characteristic different from two or three, the new Schur algebras are quasi-hereditary 1-covers of Brauer algebras, and hence the unique ‘canonical’ Schur algebras of Brauer algebras.

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Authors and Affiliations

  1. Mathematical Institute, University of Oxford, 24-29 St. Giles, Oxford, OX1 3LB, UK

    Anne Henke

  2. Institut für Algebra und Zahlentheorie, Universität Stuttgart, Pfaffenwaldring 57, 70569, Stuttgart, Germany

    Steffen Koenig

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  1. Anne Henke
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  2. Steffen Koenig
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Correspondence to Steffen Koenig.

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Henke, A., Koenig, S. Schur algebras of Brauer algebras I. Math. Z. 272, 729–759 (2012). https://doi.org/10.1007/s00209-011-0956-x

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  • DOI: https://doi.org/10.1007/s00209-011-0956-x

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