{"paper":{"title":"Auslander-Reiten combinatorics and $q$-characters of representations of affine quantum groups","license":"http://creativecommons.org/licenses/by/4.0/","headline":"","cross_cats":["math.CO","math.RA"],"primary_cat":"math.RT","authors_text":"\\'Elie Casbi, Jian-Rong Li","submitted_at":"2024-10-08T13:45:11Z","abstract_excerpt":"For each simple Lie algebra $\\mathfrak{g}$ of simply-laced type, Hernandez and Leclerc introduced a certain category $\\mathcal{C}_{\\mathbb{Z}}$ of finite-dimensional representations of the quantum affine algebra of $\\mathfrak{g}$, as well as certain subcategories $\\mathcal{C}_{\\mathbb{Z}}^{\\leq \\xi}$ depending on a choice of height function adapted to an orientation of the Dynkin graph of $\\mathfrak{g}$. In our previous work we constructed an algebra homomorphism $\\widetilde{D}_{\\xi}$ whose domain contains the image of the Grothendieck ring of $\\mathcal{C}_{\\mathbb{Z}}^{\\leq \\xi}$ under the tr"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2410.06046","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/2410.06046/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"}