On two geometric realizations of an affine Hecke algebra

Bezrukavnikov, Roman

doi:10.1007/s10240-015-0077-x

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

Publications Mathématiques de l'IHÉS, Tome 123 (2016), pp. 1-67.

Résumé

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 $G \overset{ˇ}{}$ ; 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.

MR Zbl

DOI : 10.1007/s10240-015-0077-x

Mots-clés : Full Subcategory, Monoidal Category, Tensor Category, Geometric Realization, Coherent Sheave

Affiliations des auteurs :

Bezrukavnikov, Roman ^{1, 2}

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     title = {On two geometric realizations of an affine {Hecke} algebra},
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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. http://www.numdam.org/articles/10.1007/s10240-015-0077-x/

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