Speaker: Clifton Cunningham and Qing Zhang,
We consider the Voganish project for the cubic unipotent Arthur parameter for the split exceptional group $G_2$ over a p-adic field, which was first considered by Gan-Gurevich-Jiang. After introducing this parameter $\lambda$, we consider the Vogan variety and its orbits under the action of the natural group $H_\lambda$. We then determine a smooth cover of each orbits which will help to compute the $H_\lambda$-equivariant local systems on each orbit. We also determine the principle series representation of $G_2(F)$ associated with the unramified Langlands parameter.
Location: MS 337, University of Calgary