  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.
