2020/09/08 by You-Hung Hsu, Hsu, You-Hung · 1 citation
Mathematics · Physics and Astronomy · #14M15 #18G80 #18N25 #20C08 (Secondary) #20G42 (Primary) #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #FOS: Mathematics #Nonlinear Waves and Solitons #Representation Theory (math.RT)
paper · pdf · doi:10.48550/arxiv.2009.03579
openalex publication_date 2020/09/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.