Demazure Product of the Affine Weyl Groups

Abstract

<p>The Demazure product gives a natural monoid structure on any Coxeter group. Such structure occurs naturally in many different areas in Lie Theory. This paper studies the Demazure product of an extended afhne Weyl group. The main discovery is a close connection between the Demazure product of an extended affine Weyl group and the quantum Bruhat graph of the finite Weyl group. As applications, we obtain explicit formulas on the generic Newton points and the Demazure products of elements in the lowest two-sided cell, and obtain an explicit formula on the Lusztig-Vogan map from the coweight lattice to the set of dominant coweights.</p>

Demazure乘积是定义在一般Coxeter群上的一类幺半群乘积. 它自然地出现在李理论中的不同领域中. 本文将研究仿射Weyl群上Demazur乘积. 我们的主要结果是发现了它与有限Weyl群上的量子Bruhat图之间的一个紧密联系. 作为应用, 我们给出了仿射Weyl群最低双边胞腔元素之间Demazure乘积的显示表达式, 并得到了最低双边胞腔元素的一般牛顿点以及Lusztig-Vogan映射的具体刻画.