Desiderata and Uniqueness of Local Langlands correspondence

BIMSA-YMSC Tsinghua Number Theory Seminar

Organizers：

Hansheng Diao, Heng Du, Yueke Hu, Bin Xu, Yihang Zhu, Huajie Li

Speaker：

Chi-Heng Lo (National University of Singapore）

Time：

Mon., 10:00-11:00 am, May 18, 2026

Venue：

C654, Shuangqing Complex Building A

Title：

Desiderata and Uniqueness of Local Langlands correspondence

Abstract:

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.