Base change fundamental lemma for Bernstein centers of principal series blocks
Abstract
Let $G$ be an unramified group over a $p$-adic field $F$. This article introduces a base change homomorphism for the Bernstein center of a principal series block, and proves that two functions related by this base change homomorphism are associated. This result provides new evidence for the conjecture on twisted endoscopic transfer of the stable Bernstein center proposed by T. Haines, which will be applied to a general conjecture on test functions for Shimura varieties due to R. Kottwitz and T. Haines.
Fields of Study & Subjects
Advanced Algebra and Geometry
Finite Group Theory Research
Algebraic Geometry and Number Theory
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 12 February 2026
- Language
- EN
- Document type
- Preprint