{"paper":{"title":"Isotropic Schur roots","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Charles Paquette, Jerzy Weyman","submitted_at":"2016-05-18T19:49:08Z","abstract_excerpt":"In this paper, we study the isotropic Schur roots of an acyclic quiver $Q$ with $n$ vertices. We study the perpendicular category $\\mathcal{A}(d)$ of a dimension vector $d$ and give a complete description of it when $d$ is an isotropic Schur $\\delta$. This is done by using exceptional sequences and by defining a subcategory $\\mathcal{R}(Q,\\delta)$ attached to the pair $(Q,\\delta)$. The latter category is always equivalent to the category of representations of a connected acyclic quiver $Q_{\\mathcal{R}}$ of tame type, having a unique isotropic Schur root, say $\\delta_{\\mathcal{R}}$. The underst"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.05719","kind":"arxiv","version":1},"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"}