Abstract:Let G be a reductive group over an algebraically closed field and W be its Weyl group. Using Coxeter elements, Steinberg constructed cross-sections of the adjoint quotient of G which also yield transversal slices of regular unipotent classes. In 2012, He and Lusztig constructed transversal slices using minimal length elements in elliptic conjugacy classes in W, which yield transversal...
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,...