{"paper":{"title":"Self-dual representations of Sp(4,F)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Kumar Balasubramanian","submitted_at":"2016-10-20T14:42:29Z","abstract_excerpt":"Let $F$ be a non-Archimedean local field of characteristic $0$ and $G=Sp(4,F)$. Let $(\\pi,W)$ be an irreducible smooth self-dual representation $G$. The space $W$ of $\\pi$ admits a non-degenerate $G$-invariant bilinear form $(\\,,\\,)$ which is unique up to scaling. The form $(\\,,\\,)$ is easily seen to be symmetric or skew-symmetric and we set $\\varepsilon({\\pi})=\\pm 1$ accordingly. In this paper, we show that $\\varepsilon{(\\pi)}=1$ when $\\pi$ is an Iwahori spherical representation of $G$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1610.06441","kind":"arxiv","version":1},"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"}