PBW theoretic approach to the module category of quantum affine algebras
- 주제(키워드) Cuspidal modules , quantum affine Weyl-Schur duality , Hernandez-Leclerc category , quantum affine algebra , quiver Hecke algebra
- 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, Kitashirakawa Oiwakecho, 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/000000181625
- 본문언어 영어
- Published As http://dx.doi.org/10.3792/pjaa.97.007
초록/요약
Let U-q'(g) be a quantum affine algebra of untwisted affine ADE type and let (0)(Cg) be Hernandez-Leclerc's category. For a duality datum D in (0)(Cg), we denote by F-D the quantum affine Weyl-Schur duality functor. We give a sufficient condition for a duality datum D to provide the functor F-D sending simple modules to simple modules. Moreover, under the same condition, the functor F-D has compatibility with the new invariants introduced by the authors. Then we introduce the notion of cuspidal modules in (0)(Cg), and show that all simple modules in( Cg)(0), can be constructed as the heads of ordered tensor products of cuspidal modules. We next state that the ordered tensor products of cuspidal modules have the unitriangularity property.
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