arXiv 1610.090102016-10math.RT

图代数、支配三角性和斜胞腔模

Diagram algebras, dominance triangularity, and skew cell modules

Christopher Bowman, John Enyang, Frederick Goodman

备注：: 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

摘要：

我们提出了一个抽象的框架，公理化研究的图代数。符合这一框架的代数具有类似于对称群的Hecke代数的Murphy基和Hecke正规基。我们证明了这些基之间的转移阵是优势单三角矩阵。在这种情况下，我们构建类似的斜Specht模块。这使我们能够提出一个自然的tableaux理论框架，在其中研究臭名昭著的克罗内克问题。

英文摘要：

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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