A cluster realization of Uq(sln) from quantum character varieties
成果类型：
Article
署名作者：
Schrader, Gus; Shapiro, Alexander
署名单位：
Columbia University; University of Edinburgh
刊物名称：
INVENTIONES MATHEMATICAE
ISSN/ISSBN：
0020-9910
DOI：
10.1007/s00222-019-00857-6
发表日期：
2019
页码：
799-846
关键词：
摘要：
We construct an injective algebra homomorphism of the quantum group Uq(sln+1) into a quantum cluster algebra Ln associated to the moduli space of framed PGLn+1-local systems on a marked punctured disk. We obtain a description of the coproduct of Uq(sln+1) in terms of the corresponding quantum cluster algebra associated to the marked twice punctured disk, and express the action of the R-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 of Uq(sln+1)circle times 2 given by conjugation by the R-matrix as an explicit sequence of cluster mutations, and derive a refined factorization of the R-matrix into quantum dilogarithms of cluster monomials.