Lusztig constants and endoscopyArithmetic Geometry and Representation Theory Research Seminar

by Prof. Cheng-Chiang Tsai (Academia Sinica, Taipei, Taiwan)

Tuesday Oct 27, 2026, 3:05 PM → 5:00 PM Europe/Berlin

Main Lecture Hall (Max Planck Institute for Mathematics)

In the 80’s, Lusztig described the character table of G(F_q) in terms of generalized Green functions, which arise from equivariant perverse sheaves on the unipotent variety. For large p we can pass to the Lie algebra, and Lusztig showed that the building blocks - cuspidal equivariant perverse sheaves on the nilpotent cone - are invariant under Deligne-Fourier transforms. Consequently, a corresponding function is equal to its Fourier transform up to a 4th root of unity, sometimes called a Lusztig constant.

 

I will report on the work of Wille Liu, with Wei-Hsuan Hsin and myself, that Lusztig constants are inverses of Weil indices. The method is to lift to p-adic and relate to Waldspurger's deep work on endoscopic matchings of functions associated with depth-zero cuspidal character sheaves on p-adic Lie algebras. If time permits, I will talk about applications back to p-adic groups.