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Categories over quantum affine algebras and monoidal categorification
- Title
- Categories over quantum affine algebras and monoidal categorification
- Authors
- Kashiwara, Masaki; Kim, Myungho; Oh, Se-jin; Park, Euiyong
- Ewha Authors
- 오세진
- SCOPUS Author ID
- 오세진
- Issue Date
- 2021
- Journal Title
- PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES
- ISSN
- 0386-2194
- Citation
- PROCEEDINGS OF THE JAPAN ACADEMY SERIES A-MATHEMATICAL SCIENCES vol. 97, no. 7, pp. 39 - 44
- Keywords
- Monoidal categorification; quantum affine algebra; cluster algebra; Kirillov-Reshetikhin module; T-system
- Publisher
- JAPAN ACAD
- Indexed
- SCIE; SCOPUS
- Document Type
- Article
- Abstract
- 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]).
- DOI
- 10.3792/pjaa.97.008
- Appears in Collections:
- 자연과학대학 > 수학전공 > Journal papers
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