Cluster algebra structures on module categories over quantum affine algebras
Cluster algebra structures on module categories over quantum affine algebras
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DOI：
10.1112/plms.12428
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发表时间：
2019-04
影响因子：
1.8
通讯作者：
M. Kashiwara;Myungho Kim;Se-jin Oh;E. Park
中科院分区：
文献类型：
--
作者：
M. Kashiwara;Myungho Kim;Se-jin Oh;E. Park
本文通过广义量子Schur-Weyl对偶函子，研究了量子仿射代数上有限维模的某些单模子范畴CJ $\mathcal {C}_J$的一元范畴，其Grothendieck环K(CJ) $K(\mathcal {C}_J)$上的聚类代数结构与A∞$A_\infty$型颤振Hecke代数上有限维模的范畴密切相关。特别是，当量子仿射代数为A型$A$或B型$B$时，子范畴与Hernandez-Leclerc引入的一元范畴Cg0 $\mathcal {C}_{\mathfrak {g}}^0$重合。因此，簇单项式对应的模是量子仿射代数上的实简单模。
We study monoidal categorifications of certain monoidal subcategories CJ$\mathcal {C}_J$ of finite‐dimensional modules over quantum affine algebras, whose cluster algebra structures on their Grothendieck rings K(CJ)$K(\mathcal {C}_J)$ are closely related to the category of finite‐dimensional modules over quiver Hecke algebra of type A∞$A_\infty$ via the generalized quantum Schur–Weyl duality functors. In particular, when the quantum affine algebra is of type A$A$ or B$B$ , the subcategory coincides with the monoidal category Cg0$\mathcal {C}_{\mathfrak {g}}^0$ introduced by Hernandez–Leclerc. As a consequence, the modules corresponding to cluster monomials are real simple modules over quantum affine algebras.