New Perspectives in Quantum Representation Theory

The origin of quantum representation theory dates back to Drinfeld and Jimbo’s discovery of quantum groups in 1985. From the outset, the mathematical theory was inextricably linked with various aspects of mathematical physics, including, prominently, the inverse scattering method and quantum integrability. In the 1990s, quantum representation theory was revolutionized by the introduction of powerful geometric methods, pioneered by Nakajima. At the same time, an interplay of algebraic and geometric approaches gave rise to the influential theory of q,t-characters of quantum affine algebras. Since 2000, the field has branched off in multiple directions, with seemingly endless applications.