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Diagram algebras, dominance triangularity and skew cell modules

Bowman, Christopher, Enyang, John, Goodman, Frederick (2017) Diagram algebras, dominance triangularity and skew cell modules. Journal of the Australian Mathematical Society, 104 (1). pp. 13-36. ISSN 1446-7887. E-ISSN 1446-8107. (doi:10.1017/S1446788717000179)

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https://doi.org/10.1017/S1446788717000179

Abstract

We present an abstract framework for the axiomatic study of diagram algebras. Algebras that fit this framework possess analogues of both the Murphy and seminormal bases of the Hecke algebras of the symmetric groups. We show that the transition matrix between these bases is dominance unitriangular. We construct analogues of the skew Specht modules in this setting. This allows us to propose a natural tableaux theoretic framework in which to study the infamous Kronecker problem.

Item Type: Article
DOI/Identification number: 10.1017/S1446788717000179
Subjects: Q Science
Q Science > QA Mathematics (inc Computing science)
Divisions: Faculties > Sciences > School of Mathematics Statistics and Actuarial Science
Depositing User: Christopher Bowman
Date Deposited: 31 May 2017 08:18 UTC
Last Modified: 29 May 2019 19:06 UTC
Resource URI: https://kar.kent.ac.uk/id/eprint/61893 (The current URI for this page, for reference purposes)
Bowman, Christopher: https://orcid.org/0000-0001-6046-8930
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