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Diagram algebras, dominance triangularity, and skew cell modules

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Publication details

JournalJournal of the australian mathematical society
DateE-pub ahead of print - 17 Oct 2017
DatePublished (current) - 1 Feb 2018
Issue number1
Volume104
Number of pages24
Pages (from-to)13-36
Early online date17/10/17
Original languageEnglish

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.

Bibliographical note

Funding Information:
We would like to thank the Royal Commission for the Exhibition of 1851 and EPSRC grant EP/L01078X/1 for financial support.

Publisher Copyright:
© 2017 Australian Mathematical Publishing Association Inc.

    Research areas

  • cellular algebras, diagram algebras

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