| Abstract: |
The Kazhdan-Lusztig isomorphism, relating 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 conjectures concerning the classification of tamely ramified irreducible representations. In this talk, I will recall the statement of the Kazhdan-Lusztig isomorphism and propose a conjectural relativeversion. I will focus on the case of the symmetric pair (GL2n,Sp2n), for which I can prove the relative version. I will also discuss applications to the classification of tamely ramified irreducible distinguishedrepresentations.
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