Some unipotent Arthur packets for p-adic split F4

Abstract

Let $G(k)$ be the split form of the simple exceptional p-adic group of type $F_4$, and let $\mathcal O = F_4(a_3)$ be the minimal distinguished nilpotent orbit. Our main result concerns the class of unipotent representations with cuspidal support at infinitesimal character $\Lambda$ determined by $\mathcal O$. These representations are parameterized by local systems, $\{(S, \mathcal L)\}$. We compute the characteristic cycles of the perverse sheaves $\text{IC}(S, \mathcal L)$ and determine all micro-packets in the sense of [Vo93]. In [CMBO24], the authors introduced a notion of weak Arthur packets in the p-adic setting. They conjectured that weak Arthur packets are unions of Arthur packets, in an appropriate sense. We verify that weak Arthur packets are unions of micro-packets.