{"paper":{"title":"A new involution for quantum loop algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA"],"primary_cat":"math.RT","authors_text":"Jyun-Ao Lin","submitted_at":"2014-10-25T12:37:44Z","abstract_excerpt":"In this article, we introduce a completion $\\widehat{U}^+_v(\\mathcal{L}\\mathfrak{g})$ of the positive half of the quantum affinization $U^+_v(\\mathcal{L}\\mathfrak{g})$ of a symmetrizable Kac-Moody algebra $\\mathfrak{g}$. On $\\widehat{U}^+_v(\\mathcal{L}(\\mathfrak{g}))$, we define a new \"bar-involution\" and construct the analogue Kashiwara's operators. We conjecture that the resulting pair $(\\widehat{\\mathcal{L}},\\widehat{\\mathcal{B}})$ is a crystal basis which provides the existence of the \"canonical basis\" on the (completion of the) of the positive half of the quamtum affinization."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1410.6917","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"}