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 and Grothendieck group of equivariant coherent sheaves on Steinberg variety of Langlands dual group ; 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.
@article{PMIHES_2016__123__1_0, author = {Bezrukavnikov, Roman}, title = {On two geometric realizations of an affine {Hecke} algebra}, journal = {Publications Math\'ematiques de l'IH\'ES}, pages = {1--67}, publisher = {Springer Berlin Heidelberg}, address = {Berlin/Heidelberg}, volume = {123}, year = {2016}, doi = {10.1007/s10240-015-0077-x}, mrnumber = {3502096}, zbl = {1345.14017}, language = {en}, url = {http://www.numdam.org/articles/10.1007/s10240-015-0077-x/} }
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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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