Centralisers, fixed sets and extended quotients for Weyl groups with applications to equivariant K-theory

Weyl 群的集中器、固定集和扩展商及其在等变 K 理论中的应用

• 批准号: 2770079
• 金额: --
• 依托单位: University of Southampton
• 依托单位国家: 英国
• 项目类别: Studentship
• 财政年份: 2022
• 资助国家: 英国
• 起止时间: 2022 至 无数据
• 项目状态: 未结题
• 来源: https://gtr.ukri.org/projects?ref=studentship-2770079
• 关键词: Centralisers; fixed; sets; extended; quotients

In this project we will study the structure of the centraliser of each element in the classical Weyl groups, computing their actions on the fixed sets corresponding to the elements and constructing the inertia space and extended quotient in each case. The methods will build on the previous results of the supervisors in the case of types A_n and E_6.Applications will include the computation of the equivariant rational K-theory for extended affine Weyl groups of types D_n, E7 and E_8, G_2 and F_4. In so far as it is possible, we will also study the question of whether or not the integral K-theory in these cases can contain torsion.

在这个项目中，我们将研究经典Weyl群中每个元素的中心化子的结构，计算它们在对应于元素的固定集上的作用，并在每种情况下构造惯性空间和扩展商。这些方法建立在前人对An和E6型的结果的基础上，应用于D_n，E7和E8，G2和F4型的扩张仿射Weyl群的等变有理K-理论的计算.在可能的范围内，我们还将研究在这些情况下积分K理论是否能包含挠率的问题。