Improving integrability bounds for Harish-Chandra characters

Abstract: It is a well-known result of Harish-Chandra that most invariant distributions on real and p-adic reductive groups (e.g., Fourier transforms of orbital integrals, and characters of representations) are represented by locally integrable functions on the group, and the singularities of these functions are `smoothed' by the zeroes of the Weyl discriminant. In the recent joint work with Itay Glazer and Yotam Hendel, we analyze the singularities of the inverse of the Weyl discriminant, and from that, obtain an explicit improvement on the integrability exponent of the Fourier transforms of nilpotent orbital integrals, and consequently, of characters (all these objects will be defined in the talk). I will discuss this improvement and some surprising applications, e.g., to word maps.

algebraic geometrynumber theory

Audience: researchers in the discipline

SFU NT-AG seminar

Series comments: The Number Theory and Algebraic Geometry (NT-AG) seminar is a research seminar dedicated to topics related to number theory and algebraic geometry hosted by the NT-AG group (Nils Bruin, Imin Chen, Stephen Choi, Katrina Honigs, Nathan Ilten, Marni Mishna).

We acknowledge the support of PIMS, NSERC, and SFU.

For Fall 2025, the organizers are Katrina Honigs and Peter McDonald.

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