Non-vanishing condition on Mogelin-Renard's parametrization for Arthur packets of $\mathrm U(p,q)$

Abstract

Mogelin-Renard parametrize A-packet of unitary group through cohomological induction in good parity case. Each parameter gives rise to an $A_{\mathfrak q}(\lambda)$ which is either $0$ or irreducible. Trapa proposed an algorithm to determine whether a mediocre $A_{\mathfrak q}(\lambda)$ of $\mathrm U(p, q)$ is non-zero. Based on his result, we present a further understanding of the non-vanishing condition of Mogelin-Renard's parametrization. Our criterion come out to be a system of linear constraints, and very similiar to the $p$-adic case.