Please use this identifier to cite or link to this item: https://doi.org/10.1007/s00013-011-0342-2
Title: The Schur functor on tensor powers
Authors: Lim, K.J. 
Tan, K.M. 
Keywords: Schur algebras
Schur functor
Symmetric groups
Issue Date: Feb-2012
Citation: Lim, K.J., Tan, K.M. (2012-02). The Schur functor on tensor powers. Archiv der Mathematik 98 (2) : 99-104. ScholarBank@NUS Repository. https://doi.org/10.1007/s00013-011-0342-2
Abstract: Let M be a left module for the Schur algebra S(n, r), and let s ε ℤ +. Then M ⊗s is a(S(n, rs), FS s)-bimodule, where the symmetric group S sson s letters acts on the right by place permutations. We show that the Schur functor f rs sends M ⊗s to the (FS rs, FS s)-bimodule FS rs⊗ F(SrSs). As a corollary, we obtain the image under the Schur functor of the Lie power L s(M), exterior power s(M)of M and symmetric power S s(M). © 2011 Springer Basel AG.
Source Title: Archiv der Mathematik
URI: http://scholarbank.nus.edu.sg/handle/10635/104346
ISSN: 0003889X
DOI: 10.1007/s00013-011-0342-2
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