Geodesic
On two geometric realizations of an affine Hecke algebra
Bezrukavnikov, Roman1, 2 
1 Department of Mathematics, Massachusetts Institute of Technology 77 Massachusetts ave. 02139 Cambridge MA USA
2 International Laboratory of Representation Theory and Mathematical Physics, National Research University Higher School of Economics 20 Myasnitskaya st. 101000 Moscow Russia
Publications Mathématiques de l'IHÉS, Tome 123 (2016), pp. 1-67

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The article is a contribution to the local theory of geometric Langlands duality. The main result is a categorification of the isomorphism between the (extended) affine Hecke algebra associated to a reductive group G and Grothendieck group of equivariant coherent sheaves on Steinberg variety of Langlands dual group Gˇ; this isomorphism due to Kazhdan–Lusztig and Ginzburg is a key step in the proof of tamely ramified local Langlands conjectures.

The paper is a continuation of the author’s joint work with Arkhipov, it relies on the technical material developed in a joint work with Yun.

DOI : 10.1007/s10240-015-0077-x
Keywords: Full Subcategory, Monoidal Category, Tensor Category, Geometric Realization, Coherent Sheave

Bezrukavnikov, Roman 1, 2

1 Department of Mathematics, Massachusetts Institute of Technology 77 Massachusetts ave. 02139 Cambridge MA USA
2 International Laboratory of Representation Theory and Mathematical Physics, National Research University Higher School of Economics 20 Myasnitskaya st. 101000 Moscow Russia 
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Bezrukavnikov, Roman. On two geometric realizations of an affine Hecke algebra. Publications Mathématiques de l'IHÉS, Tome 123 (2016), pp. 1-67. doi: 10.1007/s10240-015-0077-x

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