Double affine Hecke algebras and affine flag manifolds, I

TL;DR

This paper reviews the classification of simple modules of double affine Hecke algebras using K-theory of Steinberg varieties of affine type, connecting algebraic and geometric perspectives.

Contribution

It introduces a geometric approach to classifying simple modules of double affine Hecke algebras through K-theory methods.

Findings

Classification of simple modules achieved via K-theory

Connection established between algebraic modules and geometric varieties

Provides a framework for understanding affine Hecke algebra representations

Abstract

This lecture reviews the classification of simple modules of double affine Hecke algebras via the K-theory of Steinberg varieties of affine type