Diagram algebras, dominance triangularity, and skew cell modules
Representation Theory
2017-05-29 v3
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.
Cite
@article{arxiv.1610.09010,
title = {Diagram algebras, dominance triangularity, and skew cell modules},
author = {Christopher Bowman and John Enyang and Frederick Goodman},
journal= {arXiv preprint arXiv:1610.09010},
year = {2017}
}
Comments
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