Huafeng Zhang: Unitriangular R-matrices of quantum affine algebras via Theta series

Speaker
Huafeng Zhang, Université de Lille

Abstract
The universal R-matrix of the quantum affine algebra associated to a finite-dimensional simple complex Lie algebra admits a Gauss decomposition into an uper unitriangular part, an abelian part, and a lower unitriangular part. In this talk, we present a simple conjugation formula for the unitriangular R-matrices with one tensor factor evaluated at an arbitrary finite-dimensional representation of the quantum affine algebra. Our formula involves the T-series of Frenkel-Hernandez and their coproduct.