{"paper":{"title":"Non-zero condition on M{\\oe}glin-Renard's parametrization for Arthur packets of $\\mathrm U(p,q)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Chang Huang","submitted_at":"2024-09-14T08:14:55Z","abstract_excerpt":"M{\\oe}glin-Renard parametrized 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-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 $p$-adic case. This suggests a map from A-packets of r"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2409.09358","kind":"arxiv","version":2},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2409.09358/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}