{"paper":{"title":"A Common Structure in PBW Bases of the Nilpotent Subalgebra of $U_q(\\mathfrak{g})$ and Quantized Algebra of Functions","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":["math-ph","math.MP","nlin.SI"],"primary_cat":"math.QA","authors_text":"Atsuo Kuniba, Masato Okado, Yasuhiko Yamada","submitted_at":"2013-02-26T03:03:57Z","abstract_excerpt":"For a finite-dimensional simple Lie algebra $\\mathfrak{g}$, let $U^+_q(\\mathfrak{g})$ be the positive part of the quantized universal enveloping algebra, and $A_q(\\mathfrak{g})$ be the quantized algebra of functions. We show that the transition matrix of the PBW bases of $U^+_q(\\mathfrak{g})$ coincides with the intertwiner between the irreducible $A_q(\\mathfrak{g})$-modules labeled by two different reduced expressions of the longest element of the Weyl group of $\\mathfrak{g}$. This generalizes the earlier result by Sergeev on $A_2$ related to the tetrahedron equation and endows a new represent"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1302.6298","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":""},"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"}