On Special Pieces in the Unipotent Variety
On Special Pieces in the Unipotent Variety
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论单能品种中的特殊棋子
DOI：
10.1080/10586458.1999.10504405
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发表时间：
1999
期刊：
影响因子：
--
通讯作者：
G. Malle
中科院分区：
文献类型：
--
作者：
M. Geck;G. Malle
本文是使用GAP语言编写的计算机程序进行实验的结果。我们描述了一个算法，计算一组有理函数连接到有限Coxeter群W。猜想，这些有理函数应该是多项式，并且在W是定义在Fq上的Chevalley群G的Weyl群的情况下，我们的多项式在q处的值应该给出Lusztig特殊块在G的幂单簇中的Fq-有理点的数目。该算法甚至适用于复杂的反射组。我们给出了一些例子，特别是表明，我们的猜想是正确的所有类型，除了可能的Bn和Dn
This article is the result of experiments performed using computer programs written in the GAP language. We describe an algorithm which computes a set of rational functions attached to a finite Coxeter group W. Conjecturally, these rational functions should be polynomials, and in the case where W is the Weyl group of a Chevalley group G defined over Fq, the values of our polynomials at q should give the number of Fq-rational points of Lusztig's special pieces in the unipotent variety of G. The algorithm even works for complex reflection groups. We give a number of examples which show, in particular, that our conjecture is true for all types except possibly Bn and Dn