Abstract / Description of output
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)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.
the algebra automorphism of Uq(sln+1)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.
Original language | English |
---|---|
Pages (from-to) | 799-846 |
Number of pages | 48 |
Journal | Inventiones mathematicae |
Early online date | 19 Jan 2019 |
DOIs | |
Publication status | Published - 1 Jun 2019 |