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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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Relevant and petite K-types
by
Dan Barbasch
Department of Mathematics, Cornell University, Ithaca NY 14853

The determination of the unitary dual of a real reductive group is reduced to an algebraic problem by considering admissible (g , K) modules. Each K-type is endowed with a hermitian form, and the module is unitary if and only if these forms are positive definite for all K-types. Assume that G is also split, and let M be the stabilizer in K of a maximal split Cartan subalgebra. For a finite set of K-types called petite, the form is determined by the Weyl group action on the M-fixed vectors. In this talk I will discuss how to determine the Weyl group representation for a petite K-type, as well as to what extent one can find a a subset (called relevant), which gives necessary and sufficient conditions for determining the unitary dual.

Date received: July 27, 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-03.