SFU Number Theory and Algebraic Geometry Seminar: Sarah Dijols

Distinguished representations are representations of a reductive group $G$ on a vector space $V$ such that there exists a $H$-invariant linear form for a subgroup $H$ of $G$. They intervene in the Plancherel formula in a relative setting, as well as in the Sakellaridis-Venkatesh conjectures for instance. I will explain how the Geometric Lemma allows us to classify parabolically induced representations of the $p$-adic group $G_2$ distinguished by $SO_4$. In particular, I will describe a new approach, in progress, where we use the structure of the p-adic octonions and their quaternionic subalgebras to describe the double coset space $P\backslash G_2/SO_4$, where $P$ stands for the maximal parabolic subgroups of $G_2$.