English

On a converse theorem for $G_2$ over finite fields

Representation Theory 2023-02-14 v1

Abstract

In this paper, we prove certain multiplicity one theorems and define twisted gamma factors for irreducible generic cuspidal representations of split G2G_2 over finite fields kk of odd characteristic. Then we prove the first converse theorem for exceptional groups, namely, GL1GL_1 and GL2GL_2-twisted gamma factors will uniquely determine an irreducible generic cuspidal representation of G2(k)G_2(k).

Keywords

Cite

@article{arxiv.1811.10472,
  title  = {On a converse theorem for $G_2$ over finite fields},
  author = {Baiying Liu and Qing Zhang},
  journal= {arXiv preprint arXiv:1811.10472},
  year   = {2023}
}
R2 v1 2026-06-23T05:28:16.478Z