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

在这个项目中，我们将研究经典Weyl群中每个元素的中心子的结构，计算它们在与元素对应的固定集上的作用，并构造每种情况下的惯性空间和扩展商。这些方法将建立在Supervisor在A_n和E_6型情形下的先前结果的基础上，应用将包括D_n、E7和E_8、G_2和F_4型扩张仿射Weyl群的等变有理K-理论的计算。在可能的情况下，我们还将研究这些情况下的积分K-理论是否包含挠的问题。

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.