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

Sarah Dijols

paper

Parabolically induced representations of p-adic $G_{2}$ distinguished by $S O_{4}$ , I

arXiv:2203.05713

Abstract

We consider the parabolically induced representations of the symmetric space $S O_{4} \ G_{2}$ over a p-adic field using the geometric lemma when the inducing parabolic is $P_{β}$ . Using an explicit description of the embedding of $G_{2}$ in $G L_{8}$ , we characterize precisely the induced representations which are $(S O_{4}, χ)$ -distinguished, given a certain type of involutions is chosen.

arXiv commentChanged 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 G2​ distinguished by SO4​, I

Abstract

Parabolically induced representations of p-adic $G_{2}$ distinguished by $S O_{4}$ , I