{"paper":{"title":"Multivariate orthogonal Laurent polynomials and integrable systems","license":"http://creativecommons.org/publicdomain/zero/1.0/","headline":"","cross_cats":["math-ph","math.AG","math.MP","nlin.SI"],"primary_cat":"math.CA","authors_text":"Gerardo Ariznabarreta, Manuel Ma\\~nas","submitted_at":"2015-06-29T16:07:52Z","abstract_excerpt":"An ordering for Laurent polynomials in the algebraic torus $(\\mathbb C^*)^D$, inspired by the Cantero-Moral-Vel\\'azquez approach to orthogonal Laurent polynomials in the unit circle, leads to the construction of a moment matrix for a given Borel measure in the unit torus $\\mathbb T^D$. The Gauss-Borel factorization of this moment matrix allows for the construction of multivariate biorthogonal Laurent polynomials in the unit torus which can be expressed as last quasi-determinants of bordered truncations of the moment matrix.\n  Christoffel type perturbations of the measure given by the multiplic"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1506.08708","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"}