Work

On a converse theorem for $G_2$ over finite fields

Year: 2018

Type: preprint

Abstract: In this paper, we prove certain multiplicity one theorems and define twisted gamma factors for irreducible generic cuspidal representations of split $G_2$ over finite fields $k$ of odd characteristic. Then we prove the first converse theorem for exceptional groups, namely, $GL_1$ and $GL_2$-twisted gamma factors will uniquely determine an irreducible generic cuspidal representation of $G_2(k)$.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.1811.10472

Authors: Liu, Baiying, Zhang, Qing

Institutions: Purdue University West Lafayette, University of Calgary

Language: English

Topic: Advanced Algebra and Geometry

Subfield: Mathematical Physics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Science Foundation, Purdue University, National Natural Science Foundation of China, Division of Mathematical Sciences

Awards: G2352548524, On the Discrete Spectrum of Classical Groups and Converse Theorems

OpenAlex ID: W2900715597

Cites: 30

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Related to: 10