Multiplicity Formula for Cubic Unipotent Arthur Packets

Abstract

In an earlier article with Gurevich and Jiang [GGJ], we constructed the cubic unipotent Arthur packets of the exceptional group $G_2$ and showed that the discrete multiplicities of the representations in these packets are at least those predicted by Arthur's multiplicity formula. In this article, we establish the multiplicity formula by showing the reverse inequality. We also show that the parts of the discrete spectrum described by some of these packets are full near-equivalence classes