数学研究所

学术报告

表示论研讨班

Speaker: 邓太旺 教授（BIMSA）

Inviter: 聂思安 研究员

Language: Chinese

Title: Orbital integrals of GLn  over non-archimedean fields

Time&Venue: 2025年4月24日（星期四） 14: 30-16: 00 & N818

Abstract: In 2014 Zhiwei Yun introduces a local L-factor whose special value at s = 0 computes the local orbital integral of type A. These L factors are controlled by the geometry of affine Springer fibers. In this talk, we will explain a conjectural construction of an affine paving for the affine Springer fibers  based on the classical cell decomposition for compactified Jacobian by Piontkowski and show how to  deduce Yun’s local L-factor from it. In the generic case this is known by work of Gorsky, Mazin and  Oblomkov in 2024. In this case, I will explain my ongoing work with Su Tao attaching Young diagrams  to the affine cells hence giving new proof of results obtaining by the three authors.  As application, we  apply our results to deduce a conjecture by Cherednik claiming that these local L-factors satisfy the  Weil conjecture.