Journal article
Geometric representations of the formal affine Hecke algebra
G Zhao, C Zhong
Advances in Mathematics | ACADEMIC PRESS INC ELSEVIER SCIENCE | Published : 2017
Abstract
For any formal group law, there is a formal affine Hecke algebra defined by Hoffnung–Malagón-López–Savage–Zainoulline. Coming from this formal group law, there is also an oriented cohomology theory. We identify the formal affine Hecke algebra with a convolution algebra coming from the oriented cohomology theory applied to the Steinberg variety. As a consequence, this algebra acts on the corresponding cohomology of the Springer fibers. This generalizes the action of classical affine Hecke algebra on the K-theory of the Springer fibers constructed by Lusztig. We also give a residue interpretation of the formal affine Hecke algebra, which generalizes the residue construction of Ginzburg–Kaprano..
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Funding Acknowledgements
The first named author is grateful to Roman Bezrukavnikov and Valerio Toledano Laredo for encouragements, and to Valerio Toledano Laredo for introducing him to [21] and [25] so that this joint project became possible. The authors would like to thank Baptiste Calmes, Marc Levine, and Kirill Zainoulline for helpful discussions. The second named author is supported by PIMS and NSERC grants of Stefan Gille and Vladimir Chernousov. This paper is prepared when both authors are hosted by the Max Plank Institute for Mathematics in Bonn.