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arXiv · 2009.03579

A categorical action of the shifted $q=0$ affine algebra

You-Hung Hsu
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Abstract

We introduce a new algebra called the shifted $q=0$ affine algebra, which arises naturally from the study of coherent sheaves on Grassmannians and n-step partial flag varieties via a natural correspondence. It has similar presentation as the shifted quantum affine algebra defined by Finkelberg-Tsymbaliuk arXiv:1708.01795v6. We then give a definition of its categorical action and prove that there is a categorical action on the bounded derived categories of coherent sheaves on n-step partial flag varieties. Finally, as an application, we use it to construct a categorical action of the $q=0$ affine Hecke algebra on the bounded derived category of coherent sheaves on the full flag variety.

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You-Hung Hsu. 2022-04-28. A categorical action of the shifted $q=0$ affine algebra. https://arxiv.org/abs/2009.03579

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