Braid group action on the module category of quantum affine algebras
- 주제(키워드) Quantum affine algebra , quantum Grothendieck ring , braid group action , quiver Hecke algebra , R-matrix
- 주제(기타) Mathematics
- 설명문(일반) [Kashiwara, Masaki] Kyoto Univ, Inst Adv Study, Sakyo Ku, Yoshida Ushinomiya Cho, Kyoto 6068501, Japan; [Kashiwara, Masaki] Kyoto Univ, Res Inst Math Sci, Sakyo Ku, Kitashirakawa Oiwakecho, Kyoto 6068502, Japan; [Kashiwara, Masaki] Korea Inst Adv Study, Cheongryangri Dong 207-43, Seoul 02455, South Korea; [Kim, Myungho] Kyung Hee Univ, Dept Math, 26 Kyunghee Daero, Seoul 02447, South Korea; [Oh, Se-jin] Ewha Womans Univ, Dept Math, 52 Ewhayeodae Gil, Seoul 03760, South Korea; [Park, Euiyong] Univ Seoul, Dept Math, 163 Seoulsiripdaero, Seoul 02504, South Korea
- 관리정보기술 faculty
- 등재 SCIE, SCOPUS
- 발행기관 JAPAN ACAD
- 발행년도 2021
- 총서유형 Journal
- URI http://www.dcollection.net/handler/ewha/000000181557
- 본문언어 영어
- Published As http://dx.doi.org/10.3792/pjaa.97.003
초록/요약
Let g(0) be a simple Lie algebra of type ADE and let U-q' (g) be the corresponding untwisted quantum affine algebra. We show that there exists an action of the braid group B(g(0)) on the quantum Grothendieck ring K-t(g) of Hernandez-Leclerc's category C-g(0). Focused on the case of type AN 1, we construct a family of monoidal autofunctors {S-i}i is an element of Z on a localization T-N of the category of finite-dimensional graded modules over the quiver Hecke algebra of type A(infinity). Under an isomorphism between the Grothendieck ring K(T-N) of T-N and the quantum Grothendieck ring K-t(A(N-1)((1)))N, the functors {S-i}1 <= i <= N <= 1 recover the action of the braid group B(A(N-1)). We investigate further properties of these functors.
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