Dihedral long root A-packets of $p$-adic $G_2$ via theta correspondence

Raúl Alonso; Qiao He; Mishty Ray; Martí Roset

Dihedral long root A-packets of $p$-adic $G_2$ via theta correspondence

Representation Theory 2023-08-10 v1 Number Theory

Authors: Raúl Alonso , Qiao He , Mishty Ray , Martí Roset

Abstract

We construct local Arthur packets associated with a dihedral long root $A$ -parameter of a split reductive group of type $G_2$ over a nonarchimedian local field of characteristic zero. The construction relies on an exceptional correspondence for the pair $(\mathrm{PU}_3\rtimes \mathbb{Z}/2\mathbb{Z}, G_2)$ .

Keywords

local arthur packets dihedral long root a-parameter split reductive group of type g2 theta correspondence nonarchimedian local field exceptional correspondence

Cite

@article{arxiv.2308.05029,
  title  = {Dihedral long root A-packets of $p$-adic $G_2$ via theta correspondence},
  author = {Raúl Alonso and Qiao He and Mishty Ray and Martí Roset},
  journal= {arXiv preprint arXiv:2308.05029},
  year   = {2023}
}

Comments

41 pages. Comments welcome

Dihedral long root A-packets of $p$-adic $G_2$ via theta correspondence

Abstract

Keywords

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