Toward the endoscopic classification of unipotent representations of $p$-adic $G_2$

Abstract

We begin this paper by reviewing the Langlands correspondence for unipotent representations of the exceptional group of type G 2 over a p-adic field F and present it in an explicit form. Then we compute all ABV-packets, as defined in [CFM + 21] following ideas from Vogan's 1993 paper The local Langlands Conjecture, and prove that these packets satisfy properties derived from the expectation that they are generalized A-packets. We attach distributions to ABV-packets for G 2 and its endoscopic groups and study a geometric endoscopic transfer of these distributions. This paper builds on earlier work by the same authors.