일시: 4월 23일 (금) 10:00 ~ 12:00

장소: Zoom or 129동 101호

제목: Quiver Hecke algebras and unipotent quantum coordinate ring

연사: 김명호 교수 (경희대)

초록:

In this talk we will review the categorification of quantum unipotent coordinate ring $U^{-}_q(w)$ via quiver Hecke algebras. Assume that $g$ is a symmetrizable Kac-Moody algebra, $R$ is the corresponding quiver Hecke algebra, and $w$ is an element in the Weyl group of $g$. Then there exists an abelian monoidal subcategory $C_w$ of the category of finite-dimensional graded $R$-modules such that the Grothendieck ring $C_w$ is isomorphic to the unipotent quantum coordinate ring $U^{-}_q(w)$. Most of the time will be devoted to explaining this correspondence mainly following the paper "Monoidal categories associated with strata of flag varieties" by Kashiwara-Kim-Oh-Park.