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DIAGRAM ALGEBRAS, DOMINANCE TRIANGULARITY AND SKEW CELL MODULES
Published online by Cambridge University Press: 17 October 2017
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.
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- © 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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