{"paper":{"title":"Quantization of the shift of argument subalgebras in type A","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Alexander Molev, Vyacheslav Futorny","submitted_at":"2014-04-28T06:55:40Z","abstract_excerpt":"Given a simple Lie algebra $\\mathfrak{g}$ and an element $\\mu\\in\\mathfrak{g}^*$, the corresponding shift of argument subalgebra of $\\text{S}(\\mathfrak{g})$ is Poisson commutative. In the case where $\\mu$ is regular, this subalgebra is known to admit a quantization, that is, it can be lifted to a commutative subalgebra of $\\text{U}(\\mathfrak{g})$. We show that if $\\mathfrak{g}$ is of type $A$, then this property extends to arbitrary $\\mu$, thus proving a conjecture of Feigin, Frenkel and Toledano Laredo. The proof relies on an explicit construction of generators of the center of the affine vert"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1404.6879","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"}