2023 CIMPA School

Crossroads of geometry, representation theory and higher structures

David Jordan (University of Edinburgh) An introduction to geometric representation theory for quantum groups. One of the most important developments in representation theory of algebraic groups and Lie algebras in the last 30 years was the introduction of methods from algebraic geometry. By studying line bundles, differential operators, orbits, slices and other geometric constructions on spaces with group actions, such as flag varieties G/B, or coadjoint quotients g/G, we obtain deep insight into the representation theory of these structures. More recently, starting with works of Tanisaki, Backelin–Kremnitzer, Arkhipov–Gaitsgory, Varangolo–Vasserot a program of geometric representation theory for quantum groups was founded. I will survey these works and then outline some more recent developments.