Abstract The study of R-matrices, matrix solutions of the spectral (parameter-dependent) Yang-Baxter equation, was a major motivation for the discovery of quantum groups. The quasitriangular structure of these bialgebras is the origin of large classes of R-matrices. The Yang-Baxter equation has a "twisted type-B/cylindrical" counterpart: the reflection equation. Its matrix solutions, known as K...
Abstract:The FLE is a basic assertion in the quantum geometric Langlands program, proposed by Gaitsgory-Lurie, which provides a deformation of the geometric Satake equivalence to all Kac-Moody levels. We will report on a proof via the representation theory of the affine W-algebra, which is joint work in progress with Gaitsgory