Non-zero condition on M{\oe}glin-Renard's parametrization for Arthur packets of $\mathrm U(p,q)$
Representation Theory
2025-05-26 v2
Abstract
M{\oe}glin-Renard parametrized A-packet of unitary group through cohomological induction in good parity case. Each parameter gives rise to an which is either or irreducible. Trapa proposed an algorithm to determine whether a ``mediocre'' of is non-zero. Based on his result, we present a further understanding of the non-zero condition on M{\oe}glin-Renard's parametrization. Our criterion comes out to be a system of linear constraints, and has the same formulation as -adic case. This suggests a map from A-packets of real unitary group to A-packets of -adic symplectic group or special orthogonal group.
Cite
@article{arxiv.2409.09358,
title = {Non-zero condition on M{\oe}glin-Renard's parametrization for Arthur packets of $\mathrm U(p,q)$},
author = {Chang Huang},
journal= {arXiv preprint arXiv:2409.09358},
year = {2025}
}