Arthur packets for G2 and perverse sheaves on cubics

This paper begins the project of defining Arthur packets of all unipotent representations for the p-adic exceptional group G(2). Here we treat the most interesting case by defining and computing Arthur packets with component group S-3. We also show that the distributions attached to these packets are stable, subject to a hypothesis. This is done using a self-contained microlocal analysis of simple equivariant perverse sheaves on the moduli space of homogeneous cubics in two variables. We treat all other unipotent representations of p-adic G(2) in forthcoming work. (c) 2021 The Authors. Published by Elsevier Inc. This is an open access article under the CC BY-NC-ND license