Schur Algebras and Schur - Weyl Duality
نویسنده
چکیده
In this paper we study Schur-Weyl duality between the symplectic group and Brauer’s centralizer algebra over an arbitrary infinite field K. We show that the natural homomorphism from the Brauer’s centralizer algebra Bn(−2m) to the endomorphism algebra of tensor space (K) as a module over the symplectic similitude group GSp2m(K) (or equivalently, as a module over the symplectic group Sp2m(K)) is always surjective. Another surjectivitity, that of the natural homomorphism from the group algebra for GSp2m(K) to the endomorphism algebra of (K) as a module over Bn(−2m), is derived as an easy consequence of S. Oehms’ results. 2000 Mathematics Subject Classification. 16G99. The third author was supported by Alexander von Humboldt Foundation and National Natural Science Foundation of China (Project 10401005). Typeset by AMS-TEX 1
منابع مشابه
Schur-weyl Duality
Introduction 1 1. Representation Theory of Finite Groups 2 1.1. Preliminaries 2 1.2. Group Algebra 4 1.3. Character Theory 5 2. Irreducible Representations of the Symmetric Group 8 2.1. Specht Modules 8 2.2. Dimension Formulas 11 2.3. The RSK-Correspondence 12 3. Schur-Weyl Duality 13 3.1. Representations of Lie Groups and Lie Algebras 13 3.2. Schur-Weyl Duality for GL(V ) 15 3.3. Schur Functor...
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