Jon Brundan, University of Oregon
Classical representation theory via categorification
The standard approach to many sorts of representation theory related to reductive algebraic groups and semisimple Lie algebras is based on the combinatorics of the underlying Weyl group (and its Hecke algebra). In Cartan type A, there is another approach exploiting combinatorics of an underlying Kac-Moody algebra (or its quantized enveloping algebra). This was developed in examples over many decades, and fits into a unified general framework which we now call `Heisenberg categorification'. Analogous approaches are slowly emerging for the other families of classical groups (and supergroups). I will explain the general setup and some of its consequences, with examples.
MC 5501