Diagram algebras, dominance triangularity, and skew cell modules

2016/10/27 by Christopher Bowman, Bowman, Christopher, John Enyang +3
Mathematics · #FOS: Mathematics #Representation Theory (math.RT) #math.RT

paper · pdf · doi:10.48550/arxiv.1610.09010

Final version with minor editing and corrections. To appear in Journal of the Australian Mathematical Society. This paper subsumes the results of arXiv:1605.03448. arXiv admin note: text overlap with arXiv:1610.09009

arxiv created 2017/05/26 · arxiv updated 2017/05/29

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.

Citations

• Skew cell modules for diagram algebras
• The cellular second fundamental theorem of invariant theory for classical groups

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