{"paper":{"title":"On Special Unipotent Orbits and Fourier Coefficients for Automorphic Forms on Symplectic Groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.NT","authors_text":"Baiying Liu, Dihua Jiang","submitted_at":"2013-09-24T16:12:37Z","abstract_excerpt":"Fourier coefficients of automorphic representations $\\pi$ of $\\Sp_{2n}(\\BA)$ are attached to unipotent adjoint orbits in $\\Sp_{2n}(F)$, where $F$ is a number field and $\\BA$ is the ring of adeles of $F$. We prove that for a given $\\pi$, all maximal unipotent orbits, which gives nonzero Fourier coefficients of $\\pi$ are special, and prove, under a well acceptable assumption, that if $\\pi$ is cuspidal, then the stabilizer attached to each of those maximal unipotent orbits is $F$-anisotropic as algebraic group over $F$. These results strengthen, refine and extend the earlier work of Ginzburg, Ral"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1309.6238","kind":"arxiv","version":3},"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"}