Affine Springer theory and possible connections (Lecture 2)
As a pearl of geometric representation theory, generalized Springer theory is among many things essential for the character theory of finite reductive groups. The affine version of it has not been established to any extent as complete as the finite version, but many exciting results are emerging in last and mostly this decade. These results connect generalized Springer theory for graded Lie algebras, character theory of p-adic Lie algebras and groups, representations of rational and trigonometric Cherednik algebras, and knot/link invariants by Soergel bimodules. I wish to try my best to give a survey of these connections, with an emphasis on p-adic groups/Lie algebras and affine Springer fibers which I know best.
Cheng-Chiang Tsai, Stanford University