Coherent IC-sheaves on type 𝐴_{𝑛} affine Grassmannians and dual canonical basis of affine type 𝐴₁

Finkelberg, Michael; Fujita, Ryo

doi:10.1090/ert/558

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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
MathSciNet review: 4205967
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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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