OVERVIEW Representation theory is the study of the basic symmetries of mathematics and physics. The fundamental aims of geometric representation theory are to uncover the deeper geometric and categorical structures underlying the familiar objects of representation theory and harmonic analysis, and to apply the resulting insights to the resolution of classical problems. The geometric study of re...
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...