Geometry Seminar

The Kazhdan Lusztig isomorphism, which relates the affine Hecke algebra of a p-adic group to the equivariant K-theory of the Steinberg variety of its Langlands dual, played a key role in the proof of the Deligne Langlands conjecture on the classification of tamely ramified irreducible representations. For a spherical variety X, we can construct two modules over the affine Hecke algebra: the first by considering Iwahori invariant functions on X, and the second using relative Langlands duality and equivariant K-theory. It is natural to expect a relationship between these modules. I will discuss this relationship for X = GL₂ₙ/Sp₂ₙ and its application to the study of distinguished representations.