Kashiwara and Park provided a way to construct functors from the category of finite-dimensional modules over a quiver Hecke algebra to the category of finite-dimensional modules over another quiver Hecke algebra. One of the key notions in the construction is the affinization of a simple module over the (codomain) quiver Hecke algebra. In this talk I will explain the notion of affinizations in the abelian monoidal categories with certain conditions, which provides a way to construct functors from the category of finite-dimensional modules over a quiver Hecke algebra to these categories. One of the main examples of such categories is the localization of a subcategory of the finite-dimensional modules over a quiver Hecke algebra. In particular, we construct the functors $S_i$ between the localizations of the subcategories $C_{s_iw_0}$ and $C_{*,s_i}$ for arbitrary finite type quiver Hecke algebras. They are called the reflection functors since they recover the Saito reflections on crystals. This is a joint work with Masaki Kashiwara, Se-jin Oh and Euiyong Park (arxiv:2304.00238).

This seminar is a hybrid meeting.
Zoom Meeting ID: 811 7995 8722
Passcode: 529193