Hecke代数$H_n(q)$的Murphy算子积迹特征标表
The character table of the Hecke algebra $H_n(q)$ in terms of traces of products of Murphy operators
摘要：
Hecke代数$H_n(q)$的Murphy算子的迹和Murphy算子的非连续指标集的乘积的迹可以用一个简单的递归过程来计算。这些迹线被示出以确定该代数中的所有约化迹线，而这些约化迹线又确定所有其他迹线。为了说明这一过程，我们得到了一组约化迹$H_7(q)$ -最低阶Hecke代数的字符表迄今没有报道。这是之前的介绍一个明确的算法减少的痕迹的任意元素的Hecke代数成一个线性组合的痕迹的元素组成的适当定义的不相交的循环;和一个证明，提出，以使本文章合理自足，减少的痕迹只取决于一组长度的不相交的循环，它组成。
英文摘要：
The traces of the Murphy operators of the Hecke algebra $H_n(q)$, and of products of sets of Murphy operators with non-consecutive indices, can be evaluated by a straightforward recursive procedure. These traces are shown to determine all the reduced traces in this algebra, which, in turn, determine all other traces. To illustrate the procedure we obtain the set of reduced traces for $H_7(q)$ - the lowest order Hecke algebra whose character table has not hitherto been reported. This is preceded by the presentation of an explicit algorithm for the reduction of the trace of an arbitrary element of the Hecke algebra into a linear combination of traces of elements consisting of appropriately defined disjoint cycles; and of a proof, presented in order to make the present article reasonably self-contained, that a reduced trace depends only on the set of lengths of the disjoint cycles that it consists of.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
