Automorphic functionals for the minimal representations of groups of type $D_n$ and $E_n$

Nadya Gurevich, David Kazhdan

Published 2024-03-28Version 1

The minimal representation $\Pi$ of $G(\mathbb A)$ for a split simply-connected group $G$ of type $D$ or $E$ admits a realization on a space of functions $\mathcal S(X(\mathbb A))$ for a variety $X$. In this paper we write explicitly an automorphic, i.e. $G(F)$-invariant, functional on $\mathcal S(X(\mathbb A)).$