On two geometric realizations of an affine Hecke algebra

By R. Bezrukavnikov. Publications mathématiques (Bures-sur-Yvette), 2012

111 citations recorded by the source corpus.

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\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$G$\end{document} and Grothendieck group of equivariant coherent sheaves on Steinberg variety of Langlands dual group Gˇ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}${G\check {\ }}$\end{document}; 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.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/b1d311d40c50564c2aa9eb48a1ebc19b6d4de42e

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In Algebra and Number Theory

In Geometry and Topology

In Mathematical Physics

Citations in the corpus

Representations of semisimple Lie algebras in prime characteristic and the noncommutative Springer resolution (2013, background): “A more conceptual proof of braid positivity property (2) in the last lemma follows from the preprint [Bez].”