{"paper":{"title":"On Classical groups detected by the tensor third representation","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Heekyoung Hahn","submitted_at":"2015-10-10T14:39:11Z","abstract_excerpt":"Motivated by the Langlands' beyond endoscopy proposal for establishing functoriality, we study the representation $\\otimes^3$ in a setting related to the Langlands $L$-functions $L(s,\\pi,\\,\\otimes^3),$ where $\\pi$ is a cuspidal automorphic representation of $G$ where $G$ is either $\\mathrm{SO}(2n+1)$, $\\mathrm{Sp}(2n)$ and $\\mathrm{SO}(2n)$. In particular, under what conditions on partitions $\\lambda$, we examine whether or not $\\otimes^3$ detects the subgroups $\\mathbb{S}_{[\\lambda]}(G)$ for $G$ with type $B_n$ and $D_{2n}$ or $\\mathbb{S}_{\\langle\\lambda\\rangle}(G)$ for $G$ with type $C_n$. H"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1510.02944","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"}