Affine Hecke algebras arise as deformations of group algebras of affine Weyl groups. While they are often defined using a single parameter, there are also versions with several unequal parameters. In this talk, we will discuss how these unequal parameter Hecke algebras can be studied using geometric methods. We will start by reviewing the seminal work of Kazhdan-Lusztig who gave a geometric construction of affine Hecke algebras with equal parameters via equivariant K-theory and the work of Kato who extended this to the unequal parameter setting in type C. Building on these ideas, I will then present a new geometric construction that realizes affine Hecke algebras with unequal parameters uniformly across all types. Finally, we will discuss how this can be used to classify their irreducible representations.

This is an online meeting.
zoom address:
meeting ID: 858 3094 0815
passcode: 875895