A cluster realization of $$U_q(\mathfrak {sl}_{\mathfrak {n}})$$ U q ( sl n ) from quantum character varieties
A cluster realization of $$U_q(\mathfrak {sl}_{\mathfrak {n}})$$ U q ( sl n ) from quantum character varieties
复制标题
来自量子特征簇的 $$U_q(mathfrak {sl}_{mathfrak {n}})$$ U q ( sl n ) 的集群实现
DOI：
10.1007/s00222-019-00857-6
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发表时间：
2019
影响因子：
3.1
通讯作者：
Shapiro, Alexander
中科院分区：
文献类型：
--
作者：
Schrader, Gus;Shapiro, Alexander
我们构造了一个量子群的内射代数同态到一个量子簇代数，该量子簇代数与标记穿孔圆盘上的标架局域系统的模空间相关联。我们得到了的余积的一个描述，根据相应的量子簇代数相关联的标记两次穿刺磁盘，并表示的R-矩阵的作用的映射类组元素对应的半Dehn扭曲旋转一个穿刺有关其他。因此，我们实现了的代数自同构的共轭给出的R-矩阵作为一个显式序列的集群突变，并推出了一个精细的因式分解的R-矩阵的量子diamomials集群单项式。
We construct an injective algebra homomorphism of the quantum groupinto a quantum cluster algebraassociated to the moduli space of framed-local systems on a marked punctured disk. We obtain a description of the coproduct ofin terms of the corresponding quantum cluster algebra associated to the marked twice punctured disk, and express the action of theR-matrix in terms of a mapping class group element corresponding to the half-Dehn twist rotating one puncture about the other. As a consequence, we realize the algebra automorphism ofgiven by conjugation by theR-matrix as an explicit sequence of cluster mutations, and derive a refined factorization of theR-matrix into quantum dilogarithms of cluster monomials.