Schur algebras of Brauer algebras, II

A classical problem of invariant theory and of Lie theory is to determine endomorphism rings of representations of classical groups, for instance of tensor powers of the natural module (Schur–Weyl duality) or of full direct sums of tensor products of exterior powers (Ringel duality). In this article...

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Bibliographic Details
Published in:Mathematische Zeitschrift 2014-04, Vol.276 (3-4), p.1077-1099
Main Authors: Henke, Anne, Koenig, Steffen
Format: Article
Language:English
Subjects:
Mathematics
Mathematics and Statistics
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Summary:A classical problem of invariant theory and of Lie theory is to determine endomorphism rings of representations of classical groups, for instance of tensor powers of the natural module (Schur–Weyl duality) or of full direct sums of tensor products of exterior powers (Ringel duality). In this article, the endomorphism rings of full direct sums of tensor products of symmetric powers over symplectic and orthogonal groups are determined. These are shown to be isomorphic to Schur algebras of Brauer algebras as defined in Henke and Koenig (Math Z 272(3–4):729–759, 2012 ). This implies structural properties of the endomorphism rings, such as double centraliser properties, quasi-hereditary, and a universal property, as well as a classification of simple modules.
ISSN:0025-5874
1432-1823
DOI:10.1007/s00209-013-1233-y