A Geometric Realization of Affine Hecke Algebras - Lecture 3

Explore the geometric realization of affine Hecke algebras through equivariant K-theory in this advanced mathematical lecture. Delve into the Kazhdan-Lusztig and Ginzburg discovery that connects these algebraic structures to the Steinberg variety. Begin with fundamental properties of the Springer resolution and Steinberg varieties, along with an introduction to equivariant K-theory theory. Progress through the detailed explanation of how affine Hecke algebras can be geometrically realized using these mathematical frameworks. Conclude by examining the application of this geometric approach to achieve the Deligne-Langlands classification of irreducible modules for affine Hecke algebras. This lecture, part of a series on Galois representations and automorphic forms, provides deep insights into the intersection of algebraic geometry, representation theory, and K-theory, making it valuable for researchers and advanced students working in these areas of mathematics.