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arXiv · 1901.05994

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

Michael Finkelberg·Ryo Fujita
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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-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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Michael Finkelberg, Ryo Fujita. 2019-01-17. Coherent IC-sheaves on type $A_{n}$ affine Grassmannians and dual canonical basis of affine type $A_{1}$. https://doi.org/10.1090/ert%2F558

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