Categories over quantum affine algebras and monoidal categorification
- 주제(키워드) Monoidal categorification , quantum affine algebra , cluster algebra , Kirillov-Reshetikhin module , T-system
- 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, Kyoto 6068502, Japan; [Kashiwara, Masaki] Korea Inst Adv Study, 85 Hoegiro, Seoul 02455, South Korea; [Kim, Myungho] Kyung Hee Univ, Dept Math, 26 Kyungheedae Ro, 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 Seoulsiripdae Ro, Seoul 02504, South Korea
- 관리정보기술 faculty
- 등재 SCIE, SCOPUS
- 발행기관 JAPAN ACAD
- 발행년도 2021
- 총서유형 Journal
- URI http://www.dcollection.net/handler/ewha/000000182334
- 본문언어 영어
- Published As http://dx.doi.org/10.3792/pjaa.97.008
초록/요약
Let U-q'(g) be a quantum affine algebra of untwisted affine ADE type, and C-g(0) the Hernandez-Leclerc category of finite-dimensional U-q'(g)-modules. For a suitable infinite sequence (w) over cap (0) = ... s(i-1)s(i0)s(i1) ... of simple reflections, we introduce subcategories C-g([a,b]) of C-g(0) for all a <= b is an element of Z (sic) {+/-infinity}. Associated with a certain chain C of intervals in [a, b] we construct a real simple commuting family M(C) in C-g([a,b]), which consists of Kirillov-Reshetikhin modules. The category C-g([a,b]) provides a monoidal categorification of the cluster algebra K(C-g([a,b])), whose set of initial cluster variables is [M(C)]. In particular, this result gives an affirmative answer to the monoidal categorification conjecture on C-g(-) by Hernandez-Leclerc since it is C-g([-infinity,0]), and is also applicable to C-g(0) since it is C-g([-infinity,infinity]).
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