Representations and traces of the Hecke algebras Hn(q) of type An−1
Representations and traces of the Hecke algebras Hn(q) of type An−1
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DOI：
10.1063/1.529925
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发表时间：
1992
影响因子：
1.3
通讯作者：
R. King;B. G. Wybourne
中科院分区：
文献类型：
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作者：
R. King;B. G. Wybourne
引入了代数Hn(Q)中极小词的连通性类的概念，描述并实现了显式构造不可约表示矩阵的方法。在这些结果的指导下，利用Hn(Q)上的Ocneanu迹与Schur函数之间的联系，得到了计算Hn(Q)的不可约特征标的一个非常简单的公式。它们表现为将某些广义幂和对称函数与Schur函数联系起来的转移矩阵的元素。他们的评估涉及到Littlewood-Richardson规则的使用，该规则被证明适用于Hn(Q)，就像它适用于Sn.表示矩阵和字符都列在表格中。
The notion of the connectivity class of minimal words in the algebra Hn(q) is introduced and a method of explicitly constructing irreducible representation matrices is described and implemented. Guided by these results, the connection between the Ocneanu trace on Hn(q) and Schur functions is exploited to derive a very simple prescription for calculating the irreducible characters of Hn(q). They appear as the elements of the transition matrix relating certain generalized power sum symmetric functions to Schur functions. Their evaluation involves the use of the Littlewood–Richardson rule, which is proved to apply to Hn(q) just as it does to Sn. Both representation matrices and characters are tabulated.