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Terwilliger have shown that when $\\theta_i = q^{2i-d}$ and $\\theta^*_i = q^{d-2i}$ there exists an irreducible $\\boxtimes_q$-module structure on V such that the $\\"},"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":"0806.0901","kind":"arxiv","version":3},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2008-06-05T16:55:01Z","cross_cats_sorted":["math.QA","math.RA"],"title_canon_sha256":"7ef99daa92dd8bdd5b0e33b8df4e73b8036b7b1357d91ef1104354505f9537ec","abstract_canon_sha256":"e3c11f00ab4ff59816575f21552438a2fd7bc7732a269905ea5bc78b7cb41435"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:19:24.596654Z","signature_b64":"uPAP5WLFjeJM5LTSJr2OxK8AiL0zSDZPb+p6gSxhZ/FZOAXx0bj6pJg0EnFPb5kKoGeSD2I8izQ/oLpoya3CAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"32ffcfc22ecc5d65c46f530cb2ab8f060f053f147977b15f209d6a613d01160e","last_reissued_at":"2026-05-18T03:19:24.595890Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:19:24.595890Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Tridiagonal pairs and the q-tetrahedron algebra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA","math.RA"],"primary_cat":"math.RT","authors_text":"Darren Funk-Neubauer","submitted_at":"2008-06-05T16:55:01Z","abstract_excerpt":"In this paper we further develop the connection between tridiagonal pairs and the q-tetrahedron algebra $\\boxtimes_q$. 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