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

You-Hung Hsu

We introduce the shifted $q=0$ affine algebra. It is similar to the shifted
quantum affine algebra defined by Finkelberg-Tsymbaliuk arXiv:1708.01795v6. We
give a definition of its categorical action. Then we prove that there is a
categorical action of the shifted $q=0$ affine algebra on the bounded derived
categories of coherent sheaves on partial flag varieties. 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.