Work

On the local converse theorem for split SO_{2f}

Year: 2025

Type: article

Abstract: In this paper, we prove the local converse theorem for split even special orthogonal groups over a non-Archimedean local field of characteristic p ≠ 2 p\neq 2 . This is the only case left on local converse theorems of split classical groups and the difficulty is the existence of the outer automorphism. We apply a new idea by considering a certain sum of partial Bessel functions to overcome this difficulty. As a direct application, we obtain a weak rigidity theorem for irreducible generic cuspidal representations of split even special orthogonal groups.

Source: Representation Theory of the American Mathematical Society

DOI: 10.1090/ert/687

Authors: Alexander Hazeltine, Baiying Liu

Institutions: University of Michigan, Purdue University West Lafayette

Language: English

Topic: Advanced Algebra and Geometry

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: hybrid

Funder: National Science Foundation

Awards: On the Discrete Spectrum of Classical Groups and Converse Theorems, CAREER: Automorphic Forms and the Langlands Program