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Coherent IC-sheaves on type $ A_{n}$ affine Grassmannians and dual canonical basis of affine type $ A_{1}$


Authors: Michael Finkelberg and Ryo Fujita
Journal: Represent. Theory 25 (2021), 67-89
MSC (2020): Primary 17B37, 22E67; Secondary 13F60
DOI: https://doi.org/10.1090/ert/558
Published electronically: January 28, 2021
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Abstract: The convolution ring $ K^{GL_n(\mathcal {O})\rtimes \mathbb{C}^\times }(\mathrm {Gr}_{GL_n})$ was identified with a quantum unipotent cell of the loop group $ LSL_2$ in Cautis and Williams [J. Amer. Math. Soc. 32 (2019), pp. 709-778]. We identify the basis formed by the classes of irreducible equivariant perverse coherent sheaves with the dual canonical basis of the quantum unipotent cell.


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Additional Information

Michael Finkelberg
Affiliation: Department of Mathematics, National Research University Higher School of Economics, Russian Federation, 6 Usacheva st., Moscow, Russia 119048; Skolkovo Institute of Science and Technology, Moscow, Russia; and Institute for Information Transmission Problems, Russian Academy of Sciences, Moscow, Russia
Email: fnklberg@gmail.com

Ryo Fujita
Affiliation: Institut de Mathématiques de Jussieu-Paris Rive Gauche, IMJ-PRG, Université de Paris, Bâtiment Sophie Germain, F-75013 Paris, France
Email: ryo.fujita@imj-prg.fr

DOI: https://doi.org/10.1090/ert/558
Received by editor(s): February 27, 2019
Received by editor(s) in revised form: November 19, 2020
Published electronically: January 28, 2021
Additional Notes: The first author was partially funded within the framework of the HSE University Basic Research Program and the Russian Academic Excellence Project ‘5-100’. The second author was supported by Grant-in-Aid for JSPS Research Fellow (No. 18J10669) and in part by Kyoto Top Global University program.
Article copyright: © Copyright 2021 American Mathematical Society