English

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 Aq(λ)A_{\mathfrak q}(\lambda) which is either 00 or irreducible. Trapa proposed an algorithm to determine whether a ``mediocre'' Aq(λ)A_{\mathfrak q}(\lambda) of U(p,q)\mathrm U(p, q) 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 pp-adic case. This suggests a map from A-packets of real unitary group to A-packets of pp-adic symplectic group or special orthogonal group.

Keywords

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}
}