This project is maintained by ysykimura
藤田遼(京都大学理学研究科)
I-siteなんば2F S1
2017年11月29日(水) 18:00~19:30
Affine highest weight categories for quantum loop algebras of Dynkin types
For a Dynkin quiver $Q$ (i.e. Dynkin graph of a simple Lie algebra $\mathfrak{g}$ of type ADE with an orientation), Hernandez-Leclerc defined a certain good monoidal subcategory of the category of finite-dimensional modules over the quantum loop algebra of $\mathfrak{g}$ using the Auslander-Reiten quiver of $Q$. They proved that it gives a categorification of the coordinate algebra of the maximal unipotent subgroup associated with $\mathfrak{g}$. In this talk, we observe that a central completion of Hernandez-Leclerc’s category has a structure of affine highest weight category by investigating Nakajima’s homomorphism from the quantum loop algebra to the equivariant K-group of a certain Steinberg type graded quiver variety. This result can be applied to prove that Kang-Kashiwara-Kim’s generalized quantum affine Schur-Weyl duality functor between the module category of quiver Hecke algebra associated to $Q$ and Hernandez-Leclerc’s category actually gives an equivalence of monoidal categories.