Weyl-Schur duality for Cartan-type Lie superalgebra $W(n)$
نویسندگان
چکیده
منابع مشابه
Schur duality for the Cartan type Lie algebra Wn
We decompose tensor products of the defining representation of a Cartan type Lie algebra W (n) in the case where the number of tensoring does not exceed the rank of the Lie algebra. As a result, we get a kind of Schur duality between W (n) and a finite dimensional non-semisimple algebra, which is the semi-group ring of the transformation semigroup Tm .
متن کاملSchur-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...
متن کاملSchur Algebras and Schur - Weyl Duality
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...
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 کاملNew Versions of Schur-weyl Duality
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 کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Kyoto Journal of Mathematics
سال: 2001
ISSN: 2156-2261
DOI: 10.1215/kjm/1250517612