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International Conference on Representation Theory, III (ICRT III)
July 31 - August 4, 2004
Sichuan University
Chengdu, Sichuan, China

Organizers
Scientific Committee Chair: Jianpan Wang (East China Normal University, Shanghai, China) Members: Chongying Dong (California at Santa Cruz, USA) Seok-Jin Kang (Korea Institute for Advanced Study, Korea) Jianshu Li (The Hong Kong University of Science and Technology) Zongzhu Lin (Kansas, USA) Jie Xiao (Tsinghua University, Beijing, China) James Zhang (Washington, USA) Jiping Zhang (Peking University, Beijing, China) Orgenizing Committee: Chair: Liangang Peng (Sichuan, Chengdu, China) Members: Jie Du (University of New South Wales, Sydney, Australia) Ze Han (Sichuan, Chengdu, China) Yanan Lin (Xiamen, China) Youjun Tan (Sichuan, Chengdu, China) Ling Zeng (Sichuan, Chengdu, China)

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Cyclotomic Brauer algebras
by
Hebin Rui
Department of Mathematics, East China Normal University, Shanghai 200062, China

The cyclotomic Brauer algebras of type G(m, 1, n) were introduced by Haering Odenburg as a classical limit of cyclotomic Birman-Murakami-Wenzl algebras. They are cellular algebras in the sense of Graham and Lehrer. Using standard arguments on the cellular algebras, we can classify its irreducible modules over an arbitrary field. By using two functors which are some kind of induction and restriction, we can give a criterion on the semi-simplicity of a cyclotomic Brauer algebra over the complex field. When m=1, the cyclotomic Brauer algebra turns out to be the Brauer algebra. In this case, this criterion was got by H. Wenzl. We will prove that the Brauer algebra Bn(d) is semisimple if and only if all cell modules D(1, l) are irreducible as Bk(d)-modules. Here 2 £ k £ n and l is a partition of k-2. Using certain results due to Doran-Wales-Hanlon together with some arguments on cellular algebras, we can give algorithm to determine all the pairs (n, d) such that Bn(d) is semi-simple.

The talk is based on the papers:

1. Hebing Rui and Weihua Yu: "On the semi-simplicity of the cyclotomic Brauer algberas" , 2003.

2. Hebing Rui: Semisimple Brauer algebras, 2004.

Date received: July 28, 2004

Copyright © 2004 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # caoh-24.