MS Seminar (Mathematics - String Theory)

Speaker: Ting Xue (University of Melbourne)
Title: Graded Lie algebras, character sheaves, and representations of DAHAs
Date: Fri, Feb 14, 2020, 13:15 - 14:45
Place: Seminar Room B
Blackboard: (Blackboard talk)
Abstract: We describe a strategy for classifying character sheaves in the setting of graded Lie algebras. Via a nearby cycle construction we show that the character sheaves are IC-sheaves associated to irreducible representations of Hecke algebras of complex reflection groups at roots of unity. We will explain how our work is connected to recent work of Lusztig and Yun where (Fourier transforms of) character sheaves are parametrized by irreducible representations of certain graded double affine Hecke algebras (DAHA). If time permits, we will also explain a Schur-Weyl duality conjecture arising from the geometric construction of rational Cherednik algebra modules of Oblomkov and Yun using affine Springer fibres. This is based on joint work with Kari Vilonen and partly with Misha Grinberg.