Equivariant K-theory of generalized Steinberg varieties

TL;DR

This paper computes the equivariant K-theory of generalized Steinberg varieties, connecting algebraic geometry with affine Hecke algebras, and introduces Kazhdan-Lusztig structures in this context.

Contribution

It provides a new description of equivariant K-groups of generalized Steinberg varieties using extended affine Hecke algebras and defines Kazhdan-Lusztig bases and involutions for these groups.

Findings

Explicit description of equivariant K-groups in terms of affine Hecke algebra

Introduction of Kazhdan-Lusztig bases for these K-groups

Application to interpolating between Steinberg variety and nilpotent cone

Abstract

We describe the equivariant K-groups of a family of generalized Steinberg varieties that interpolates between the Steinberg variety of a reductive, complex algebraic group and its nilpotent cone in terms of the extended affine Hecke algebra and double cosets in the extended affine Weyl group. As an application, we use this description to define Kazhdan-Lusztig "bar" involutions and Kazhdan-Lusztig bases for these equivariant K-groups.