B~ 2型仿射Weyl群的Kazhdan-Lusztig系数

Pub Date : 2021-11-08 DOI:10.1142/s1005386721000420

Ge Feng, Liping Wang

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引用次数: 0

摘要

设[公式:见文]为类型为[公式:见文]的仿射Weyl群，我们在其上考虑从[公式:见文]到[公式:见文]的长度函数[公式:见文]和Bruhat序[公式:见文]。对于[公式:见文]中的[公式:见文]，设[公式:见文]为Kazhdan-Lusztig多项式[公式:见文]中[公式:见文]的系数。我们为[Formula: see text]和[Formula: see text]确定了一些[Formula: see text]，其中[Formula: see text]是[Formula: see text]的最低的双面单元格，[Formula: see text]是较高的。进一步，我们得到了左串和右串的一些结果以及前导系数的一些性质。

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Some Kazhdan–Lusztig Coefficients of Affine Weyl Group of Type B~ 2

Let [Formula: see text] be the affine Weyl group of type [Formula: see text], on which we consider the length function [Formula: see text] from [Formula: see text] to [Formula: see text] and the Bruhat order [Formula: see text]. For [Formula: see text] in [Formula: see text], let [Formula: see text] be the coefficient of [Formula: see text] in Kazhdan–Lusztig polynomial [Formula: see text]. We determine some [Formula: see text] for [Formula: see text] and [Formula: see text], where [Formula: see text] is the lowest two-sided cell of [Formula: see text] and [Formula: see text] is the higher one. Furthermore, we get some consequences using left or right strings and some properties of leading coefficients.

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