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DIAGRAM ALGEBRAS, DOMINANCE TRIANGULARITY AND SKEW CELL MODULES

Published online by Cambridge University Press:  17 October 2017

CHRISTOPHER BOWMAN
Affiliation:
School of Mathematics, Statistics and Actuarial Science, University of Kent, Canterbury CT2 7FS, UK email [email protected]
JOHN ENYANG
Affiliation:
Department of Mathematics, City University London, London, UK email [email protected]
FREDERICK GOODMAN*
Affiliation:
Department of Mathematics, University of Iowa, Iowa City, IA 52242, USA email [email protected]
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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.

Type
Research Article
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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