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

Clifton Cunningham; Andrew Fiori; Qing Zhang

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

Representation Theory 2021-01-26 v2 Algebraic Geometry Number Theory

Authors: Clifton Cunningham , Andrew Fiori , Qing Zhang

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.

Keywords

unipotent representations p-adic g2 langlands correspondence abv-packets endoscopic groups geometric endoscopic transfer

Cite

@article{arxiv.2101.04578,
  title  = {Toward the endoscopic classification of unipotent representations of $p$-adic $G_2$},
  author = {Clifton Cunningham and Andrew Fiori and Qing Zhang},
  journal= {arXiv preprint arXiv:2101.04578},
  year   = {2021}
}

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

Abstract

Keywords

Cite

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