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

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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.