Cellularity of endomorphism algebras of Young permutation modules

JOURNAL OF ALGEBRA

卷:572

Article

Donkin, Stephen¹ 

[1] Univ York, Dept Math, York YO10 5DD, N Yorkshire, England

关键词: Cellular;    Endomorphism algebra;    Young permutation module;   

DOI  :  10.1016/j.jalgebra.2020.11.022

来源: Elsevier

【 摘 要 】

Let E be an n-dimensional vector space. Then the symmetric group Sym(n) acts on E by permuting the elements of a basis and hence on the r-fold tensor product E-circle times r. Bowman, Doty and Martin ask, in [1], whether the endomorphism algebra End(sym(n)) (E-circle times r) is cellular. The module E-circle times r is the permutation module for a certain Young Sym(n)-set. We shall show that the endomorphism algebra of the permutation module on an arbitrary Young Sym(n)-set is a cellular algebra. We determine, in terms of the point stabilisers which appear, when the endomorphism algebra is quasi-hereditary. (C) 2020 Elsevier Inc. All rights reserved.

【 授权许可】

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