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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1710.09156","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.NT","submitted_at":"2017-10-25T10:31:45Z","cross_cats_sorted":[],"title_canon_sha256":"d3e0a0db583adda8e5face1f8016d2c3f1c3f505b1bdeff8a1b22d2b8f5213ba","abstract_canon_sha256":"59a81ecd0a8c51956d3cd0c67e049dd54f0b785455fa5dfb34bdf10d64bdb4da"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:20:38.678240Z","signature_b64":"GrKIb7iFoNO7es7xoN9+voFd+I6O1fg9tCrrcAMGNM37k2wG2pZia+LPQNfMJyW7QZR2Jvp8wTNp1ozXWSeWAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"798248831c0912c2ee8a79fe799af87a7d5647df42f5e9eb478b313876a5fa02","last_reissued_at":"2026-05-18T00:20:38.677576Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:20:38.677576Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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 $N\\in \\mathbb{N}$. 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