Abstract:

In this first lecture, I will review the Springer theory of equivariant perverse sheaves on graded Lie algebras, mostly due to Lusztig in the 80s and 90s. Lusztig has proven that the equivariant simple perverse sheaves on the graded Lie algebra can be partitioned into Harish-Chandra series, each generated by a cuspidal local system via the procedure of parabolic induction; in addition, each Harish-Chandra series is constrolled by an affine Hecke algebra. If time permits, we will mention some of the extensions of Lusztig's theory developed during the past two decades.

The auditor is assumed to have basic acquaintance with algebraic groups and perverse sheaves / D-modules.