Graded Lie algebras, character sheaves, and representations of DAHAs

Abstract: We describe a strategy for classifying character sheaves in the setting of graded Lie algebras. Via a nearby cycle construction we show that irreducible representations of Hecke algebras of complex reflection groups at roots of unity enter the description of character sheaves. We will explain connection to the work of Lusztig and Yun where (Fourier transforms of) character sheaves are parametrized by irreducible representations of trigonometric double affine Hecke algebras (DAHA). We will discuss some conjectures arising from this connection, which relate finite dimensional irreducible representations of trigonometric DAHAs to irreducible representations of Hecke algebras. This is based on joint work with Kari Vilonen and partly with Misha Grinberg.

representation theory

Audience: researchers in the topic

MIT Lie groups seminar

Series comments: Description: Research seminar on Lie groups

This seminar will take place entirely online: Zoom Meeting Link. You should be able to watch live video at this link. Your microphone will be muted, but you are welcome to unmute it (microphone icon on the lower left of the Zoom window, perhaps visible only when you put your mouse near there) to ask a question.