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arXiv · 2203.05713

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

Sarah Dijols
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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.

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Sarah Dijols. 2022-03-11. Parabolically induced representations of p-adic $G_2$ distinguished by $SO_4$, I. https://arxiv.org/abs/2203.05713

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