{"paper":{"title":"Logarithmic Link Invariants of $\\overline{U}_q^H(\\mathfrak{sl}_2)$ and Asymptotic Dimensions of Singlet Vertex Algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["hep-th","math.GT","math.NT","math.RT"],"primary_cat":"math.QA","authors_text":"Antun Milas, Matt Rupert, Thomas Creutzig","submitted_at":"2016-05-18T15:54:58Z","abstract_excerpt":"We study relationships between the restricted unrolled quantum group $\\overline{U}_q^H(\\mathfrak{sl}_2)$ at $2r$-th root of unity $q=e^{\\pi i/r}, r \\geq 2$, and the singlet vertex operator algebra $\\mathcal M(r)$. We use deformable families of modules to efficiently compute $(1, 1)$-tangle invariants colored with projective modules of $\\overline{U}_q^H(\\mathfrak{sl}_2)$. These relate to the colored Alexander tangle invariants studied in [ADO, M1]. It follows that the regularized asymptotic dimensions of characters of $\\mathcal M(r)$ coincide with the corresponding modified traces of open Hopf "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.05634","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"}