{"paper":{"title":"A Graph Theoretic Method for Determining Generating Sets of Prime Ideals in Quantum Matrices","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.QA","authors_text":"Karel Casteels","submitted_at":"2009-07-09T17:12:37Z","abstract_excerpt":"We take a graph theoretic approach to the problem of finding generators for those prime ideals of $\\mathcal{O}_q(\\mathcal{M}_{m,n}(\\mathbb{K}))$ which are invariant under the torus action ($\\mathbb{K}^*)^{m+n}$. Launois \\cite{launois3} has shown that the generators consist of certain quantum minors of the matrix of canonical generators of $\\mathcal{O}_q(\\mathcal{M}_{m,n}(\\mathbb{K}))$ and in \\cite{launois2} gives an algorithm to find them. In this paper we modify a classic result of Lindstr\\\"{o}m \\cite{lind} and Gessel-Viennot~\\cite{gv} to show that a quantum minor is in the generating set for"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0907.1617","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"}