Toward the endoscopic classification of unipotent representations of p-adic G₂

2021/01/12 by Cunningham, Clifton, Fiori, Andrew, Zhang, Qing · 1 citation
#11F70 (Primary) 22E50 #32S30 #32S60 (Secondary) #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2101.04578

Abstract

We begin this paper by reviewing the Langlands correspondence for unipotent representations of the exceptional group of type G₂ 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 G₂ and its endoscopic groups and study a geometric endoscopic transfer of these distributions. This paper builds on earlier work by the same authors.

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