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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

A characteristic free approach to Brauer algebras


Authors: Steffen König and Changchang Xi
Journal: Trans. Amer. Math. Soc. 353 (2001), 1489-1505
MSC (1991): Primary 16D25, 16G30, 20G0; Secondary 57M25, 81R05
Published electronically: December 18, 2000
MathSciNet review: 1806731
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Abstract | References | Similar Articles | Additional Information

Abstract:

Brauer algebras arise in representation theory of orthogonal or symplectic groups. These algebras are shown to be iterated inflations of group algebras of symmetric groups. In particular, they are cellular (as had been shown before by Graham and Lehrer). This gives some information about block decomposition of Brauer algebras.


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Additional Information

Steffen König
Affiliation: Fakultät für Mathematik, Universität Bielefeld, Postfach 100131, D-33501 Bielefeld, Germany
Address at time of publication: Department of Mathematics and Computer Science, University of Leicester, University Road, Leicester, LE1 7RH, United Kingdom
Email: sck5@mcs.le.ac.ak

Changchang Xi
Affiliation: Department of Mathematics, Beijing Normal University, 100875 Beijing, People’s Republic of China
Email: xicc@bnu.edu.cn

DOI: http://dx.doi.org/10.1090/S0002-9947-00-02724-0
PII: S 0002-9947(00)02724-0
Keywords: Brauer algebras, orthogonal groups, symplectic groups, cellular algebras
Received by editor(s): January 26, 1998
Received by editor(s) in revised form: January 13, 2000
Published electronically: December 18, 2000
Additional Notes: Both authors have obtained support from the Volkswagen Foundation (Research in Pairs Programme of the Mathematical Research Institute Oberwolfach). S. König also obtained support from Beijing Normal University during his stay in Beijing in May 1997, when most of this paper has been written. C. C. Xi also obtained support from the Young Teacher Foundation of Chinese Educational Committee and from NSF of China (Grant No. 19831070).
Article copyright: © Copyright 2000 American Mathematical Society