{"paper":{"title":"SL2 tilting modules in the mixed case","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.QA"],"primary_cat":"math.RT","authors_text":"Daniel Tubbenhauer, Jieru Zhu, Louise Sutton, Paul Wedrich","submitted_at":"2021-05-17T10:52:03Z","abstract_excerpt":"Using the non-semisimple Temperley-Lieb calculus, we study the additive and monoidal structure of the category of tilting modules for $\\mathrm{SL}_{2}$ in the mixed case. This simultaneously generalizes the semisimple situation, the case of the complex quantum group at a root of unity, and the algebraic group case in positive characteristic. We describe character formulas and give a presentation of the category of tilting modules as an additive category via a quiver with relations. Turning to the monoidal structure, we describe fusion rules and obtain an explicit recursive description of the a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2105.07724","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":""},"integrity":{"clean":true,"summary":{"advisory":0,"critical":0,"by_detector":{},"informational":0},"endpoint":"/pith/2105.07724/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"}