The explicit Local Langlands Correspondence for $G_2$ II: character formulas and stability

Abstract

We write down character formulas for representations of $G_2$ considered in Aubert-Xu, and show that stability for $L$-packets uniquely pins down the Local Langlands Correspondence constructed in Aubert-Xu, thus proving unique characterization of the LLC \textit{loc.cit.}

21 pages