On a converse theorem for $G_2$ over finite fields

Baiying Liu; Qing Zhang

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arXiv · 1811.10472

On a converse theorem for $G_2$ over finite fields

Baiying Liu·Qing Zhang

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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 $G_2(k)$.

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BibTeX RIS

Baiying Liu, Qing Zhang. 2018-11-26. On a converse theorem for $G_2$ over finite fields. https://arxiv.org/abs/1811.10472

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