Permutation modules for cellularly stratified algebras

JOURNAL OF PURE AND APPLIED ALGEBRA

卷:224

Article

Paul, Inga¹ 

[1] Univ Stuttgart, Inst Algebra & Zahlentheorie, Pfaffenwaldring 57, D-70569 Stuttgart, Germany

关键词: Cellular algebras;    Permutation modules;    Young modules;    Partition algebras;   

DOI  :  10.1016/j.jpaa.2020.106412

来源: Elsevier

【 摘 要 】

Permutation modules play an important role in the representation theory of the symmetric group. Hartmann and Paget defined permutation modules for Brauer algebras. We generalise their construction to a wider class of algebras, namely cellularly stratified algebras, satisfying certain conditions. We give a decomposition into indecomposable summands, the Young modules, and show that permutation modules and Young modules admit cell filtrations (with well-defined filtration multiplicities). Partition algebras are shown to satisfy the given conditions, provided the characteristic of the underlying field is large enough. Thus we obtain a definition of permutation modules for partition algebras as an application. (C) 2020 Elsevier B.V. All rights reserved.

【 授权许可】

Free