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DIAGRAM ALGEBRAS, DOMINANCE TRIANGULARITY AND SKEW CELL MODULES

Part of: Linear algebraic groups and related topics Algebraic combinatorics

Published online by Cambridge University Press:  17 October 2017

CHRISTOPHER BOWMAN ,
JOHN ENYANG  and
FREDERICK GOODMAN Open the ORCID record for FREDERICK GOODMAN [Opens in a new window]
CHRISTOPHER BOWMAN
Affiliation:
School of Mathematics, Statistics and Actuarial Science, University of Kent, Canterbury CT2 7FS, UK email C.D.Bowman@kent.ac.uk
JOHN ENYANG
Affiliation:
Department of Mathematics, City University London, London, UK email john.enyang.1@city.ac.uk
FREDERICK GOODMAN*
Affiliation:
Department of Mathematics, University of Iowa, Iowa City, IA 52242, USA email frederick-goodman@uiowa.edu
*
✉frederick-goodman@uiowa.edu
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Abstract

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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.

Keywords

cellular algebrasdiagram algebras

MSC classification

Primary: 20G05: Representation theory
Secondary: 05E10: Combinatorial aspects of representation theory
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 104 , Issue 1 , February 2018 , pp. 13 - 36
Copyright
© 2017 Australian Mathematical Publishing Association Inc. 

Footnotes

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

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