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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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...
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After reviewing classical Schur-Weyl duality, we present some other contexts which enjoy similar features, relating to Brauer algebras and classical groups. 1. Classical Schur-Weyl duality 1.1. Schur’s double-centralizer result. Consider the vector space V = C. The symmetric group Sr acts naturally on its r-fold tensor power V , by permuting the tensor positions. This action obviously commutes ...
متن کاملSchur–weyl Duality for Orthogonal Groups
We prove Schur–Weyl duality between the Brauer algebra Bn(m) and the orthogonal group Om(K) over an arbitrary infinite field K of odd characteristic. If m is even, we show that each connected component of the orthogonal monoid is a normal variety; this implies that the orthogonal Schur algebra associated to the identity component is a generalized Schur algebra. As an application of the main res...
متن کاملBrauer Algebras, Symplectic Schur Algebras and Schur-weyl Duality
In this paper we prove the Schur-Weyl duality between the symplectic group and the Brauer algebra over an arbitrary infinite field K. We show that the natural homomorphism from the Brauer algebra Bn(−2m) to the endomorphism algebra of the tensor space (K2m)⊗n as a module over the symplectic similitude group GSp2m(K) (or equivalently, as a module over the symplectic group Sp2m(K)) is always surj...
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ژورنال
عنوان ژورنال: Memoirs of the American Mathematical Society
سال: 2017
ISSN: 0065-9266,1947-6221
DOI: 10.1090/memo/1157