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Explore the geometric realization of affine Hecke algebras through equivariant K-theory in this mathematical lecture delivered at the Centre International de Rencontres Mathématiques. Begin with fundamental properties of the Springer resolution and Steinberg varieties, along with an introduction to equivariant K-theory concepts. Discover the groundbreaking geometric realization of affine Hecke algebras developed by Kazhdan-Lusztig and Ginzburg using the Steinberg variety. Learn how this geometric approach led to the Deligne-Langlands classification of irreducible modules for affine Hecke algebras, providing crucial insights into representation theory. The lecture forms part of the thematic meeting on "Galois representations and automorphic forms" and serves as the first installment in a comprehensive series examining these advanced algebraic structures from a geometric perspective.
