Seminar of Algebra

The constructible Langlands correspondence establishes a profound connection between the representation theory of GL_n(Q_p) and the theory of perverse sheaves/D-modules on certain quiver varieties.The goal of this talk is to give a gentle and explicit introduction to these themes and to a new class of interesting conjectures due to Minguez and Lapid. They go beyond the classical correspondence and relate representation-theoretic phenomena with the behavior of irreducible components in Lustzig’s Characteristic variety of type A. Finally, we will propose a set of new conjectures, suggesting a connection to intertwining operators, and present some evidence for their validity.