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On two geometric realizations of an affine Hecke algebra
Roman Bezrukavnikov1, 2 idref
1Department of Mathematics, Massachusetts Institute of Technology 77 Massachusetts ave. 02139 Cambridge MA USA
2International 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, Volume 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.

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

Roman Bezrukavnikov  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 
Roman Bezrukavnikov. On two geometric realizations of an affine Hecke algebra. Publications Mathématiques de l'IHÉS, Volume 123 (2016), pp. 1-67. doi: 10.1007/s10240-015-0077-x
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