{"paper":{"title":"On the dependence of the local Rankin-Selberg gamma factors of $\\textrm{Sp}_{2n}\\times \\textrm{GL}_m$ on $\\psi$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.NT","authors_text":"Qing Zhang","submitted_at":"2016-01-28T01:42:39Z","abstract_excerpt":"Let $F$ be a $p$-adic field and $\\pi$ be an irreducible smooth representation of $\\textrm{Sp}_{2n}(F)$. In this paper, we show that if $\\pi$ and $\\pi^\\kappa$ are both generic for a common generic character of the maximal unipotent of a fixed Borel, then $\\pi\\cong \\pi^\\kappa$, where $\\pi^\\kappa$ is the representation induced by the conjugation action of an element $\\kappa\\in \\textrm{GSp}_{2n}(F)$. This result is a consequence of the standard local Langlands conjecture and local Gan-Gross-Prasad conjecture. As a consequence, we extend the dependence relation of the local Rankin-Selberg gamma fac"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1601.07618","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":""},"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"}