Parabolically induced representations of p-adic $G_2$ distinguished by $SO_4$, I

Sarah Dijols

Parabolically induced representations of p-adic $G_2$ distinguished by $SO_4$, I

Representation Theory 2023-01-12 v4 Number Theory

Authors: Sarah Dijols

Abstract

We consider the parabolically induced representations of the symmetric space $SO_4\backslash G_2$ over a p-adic field using the geometric lemma when the inducing parabolic is $P_{\beta}$ . Using an explicit description of the embedding of $G_2$ in $GL_8$ , we characterize precisely the induced representations which are $(SO_4, \chi)$ -distinguished, given a certain type of involutions is chosen.

Keywords

p-adic groups parabolically induced representations g2 so4 distinguished representations geometric lemma

Cite

@article{arxiv.2203.05713,
  title  = {Parabolically induced representations of p-adic $G_2$ distinguished by $SO_4$, I},
  author = {Sarah Dijols},
  journal= {arXiv preprint arXiv:2203.05713},
  year   = {2023}
}

Comments

Changed slightly the Proposition 4.1 and corrected an error in its application in the main Theorem, deleted Lemmas 4.1 and 4.2 which were not used later in the paper, changed the argumentation in Section 8.1

Parabolically induced representations of p-adic $G_2$ distinguished by $SO_4$, I

Abstract

Keywords

Cite

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