- BIMSA-YMSC 清华数论讨论班

Desiderata and Uniqueness of Local Langlands correspondence

组织者

刁晗生 , 杜衡 , 胡悦科 , Bin Xu , Yihang Zhu

演讲者

羅啟恒

时间

2026年05月18日 10:00 至 11:00

地点

Shuangqing-C654

摘要

The local Langlands conjecture predicts a "canonical" bijection between the set of smooth irreducible representations of a p-adic reductive algebraic group G and the set of enhanced L-parameters for G, a bijection known as the local Langlands correspondence (LLC). While several constructions of the LLC exist in the literature, each typically applies to particular groups or specific classes of representations. Comparing these various constructions is a subtle and challenging problem. In this talk, I will present joint work with Tasho Kaletha and Cheng-Chiang Tsai, in which we collect a list of desiderata for the LLC for general p-adic groups from the literature. Our main theorem establishes that, when p is sufficiently large, any LLC satisfying these desiderata is unique (if it exists). This provides a unified framework for comparing different LLC.