{"paper":{"title":"The Hecke algebras for the orthogonal group $SO(2,3)$ and the paramodular group of degree $2$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NT","authors_text":"Aloys Krieg, Jonas Gallenk\\\"amper","submitted_at":"2017-10-25T10:31:45Z","abstract_excerpt":"In this paper we consider the integral orthogonal group with respect to the quadratic form of signature $(2,3)$ given by $\\left(\\begin{smallmatrix}\n  0 & 1 \\\\ 1 & 0\n  \\end{smallmatrix}\\right) \\perp \\left(\\begin{smallmatrix}\n  0 & 1 \\\\ 1 & 0\n  \\end{smallmatrix}\\right) \\perp (-2N)$ for squarefree $N\\in \\mathbb{N}$. The associated Hecke algebra is commutative and the tensor product of its primary components, which turn out to be polynomial rings over $\\mathbb{Z}$ in $2$ algebraically independent elements.\n  The integral orthogonal group is isomorphic to the paramodular group of degree $2$ and lev"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1710.09156","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"}