{"paper":{"title":"Triangular Decomposition of the Crystal Lattice of Quantized Function Algebras: Revisited","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA","math.RT"],"primary_cat":"math.QA","authors_text":"Ayan Dey","submitted_at":"2026-03-23T12:02:02Z","abstract_excerpt":"Let $\\g$ be a simple complex Lie algebra of type $G_2$, $F_4$, or $E_8$, and let $G$ be the unique connected simply connected complex Lie group with $\\mathrm{Lie}(G)=\\g$ and compact real form $K$. We prove a triangular decomposition theorem for the lower crystal lattice $\\OAztG$ of the quantized function algebra $\\OtG$, establishing that $\\OAztG=A_0\\text{-alg}<\\RAzp \\cup \\RAzm>.$ This extends the triangular decomposition recently obtained for types $A_n, B_n, C_n, D_n, E_6$, and $E_7$ in~\\cite{DDPa} to all simple complex Lie algebras. As a consequence, we obtain: (i) the inclusion $\\OAztG\\subs"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2603.21868","kind":"arxiv","version":2},"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/2603.21868/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"}