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

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.

54 pages. Comments are welcome. Some major changes in v2 : I. Revise the introduction. II. Omit and reduce some proofs in order to shorten the article. III. Add Section 5.1 for an overview of proof for the main theorem and Section 5.5 for calculations on the Grothendieck groups. IV. Rewrite the proof for Theorem 6.3. V. Update the references

References in corpus (3)

• 2-Kac-Moody algebras
• Vertex operators and 2-representations of quantum affine algebras
• Rigidity in higher representation theory