{"paper":{"title":"On the affine Springer fibers inside the invariant center of the small quantum group","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.AG","math.QA"],"primary_cat":"math.RT","authors_text":"Anna Lachowska, Nicolas Hemelsoet, Oscar Kivinen","submitted_at":"2022-05-19T17:07:39Z","abstract_excerpt":"Let $\\mathfrak{u}_\\zeta^\\vee$ denote the small quantum group associated with a simple Lie algebra $\\mathfrak{g}^\\vee$ and a root of unity $\\zeta$. In [9], a geometric realization of $Z(\\mathfrak{u}_\\zeta^\\vee)^{G^\\vee}$, the $G^\\vee$-invariant part of the center of $\\mathfrak{u}_\\zeta^\\vee$, was proposed. We compute the dimension of the geometric subalgebra of the center and in the case where $G=SL_n$, we study a bigraded refinement of the result."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2205.09700","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2205.09700/integrity.json","findings":[],"available":true,"detectors_run":[],"snapshot_sha256":"c28c3603d3b5d939e8dc4c7e95fa8dfce3d595e45f758748cecf8e644a296938"},"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"}