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By a theorem due to Ovsienko, for each tableau $T(v)$ there exists a finite number of nonisomorphic irreducible Gelfand-Tsetlin modules with $\\chi_v$ in its support, though explicit examples of such modules are only known for special families of characters. In this article we build a family of Gelfand-Tsetlin modules parametrized by characters, such that each character appears in its corresponding module. We also find the support of these modules, wit"},"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":"1705.10731","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.RT","submitted_at":"2017-05-30T16:34:45Z","cross_cats_sorted":[],"title_canon_sha256":"645616013527d254dcc7640115154bd1214d46cd29fa72ddae451c87626e01ba","abstract_canon_sha256":"88828c7e3ab7f8183807b65f9eb19e1488c99845e5c0843338d72973c65b77b0"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:39:23.738605Z","signature_b64":"ZRLoxD2FP8Ml/tNa6u4/vaO1eHckcSjj85cOqprYto5VjptmXxcmNxBrGkqJ2V/GlPFQv1gm0lqdjIn+p0JiCg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"2abcd48cb7cbac11aed799a6ce2eaff16f416eba88c19e3a17f4f2dce629a21b","last_reissued_at":"2026-05-18T00:39:23.737997Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:39:23.737997Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Gelfand-Tsetlin modules over $\\mathfrak{gl}(n,\\mathbb C)$ with arbitrary characters","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Luis Enrique Ram\\'irez, Pablo Zadunaisky","submitted_at":"2017-05-30T16:34:45Z","abstract_excerpt":"A Gelfand-Tsetlin tableau $T(v)$ induces a character $\\chi_v$ of the Gelfand-Tsetlin subalgebra $\\Gamma$ of $U = U(\\mathfrak{gl}(n,\\mathbb C))$. By a theorem due to Ovsienko, for each tableau $T(v)$ there exists a finite number of nonisomorphic irreducible Gelfand-Tsetlin modules with $\\chi_v$ in its support, though explicit examples of such modules are only known for special families of characters. In this article we build a family of Gelfand-Tsetlin modules parametrized by characters, such that each character appears in its corresponding module. 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