{"paper":{"title":"Multiplicaton formulas and canonical basis for quantum affine gl_n","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RA","math.RT"],"primary_cat":"math.QA","authors_text":"Jie Du, Zhonghua Zhao","submitted_at":"2016-08-04T04:26:09Z","abstract_excerpt":"We will give a representation-theoretic proof for the multiplication formula in the Ringel-Hall algebra ${\\frak H}_\\Delta(n)$ of a cyclic quiver $\\Delta(n)$ given in \\cite[Thm~4.5]{DuFu2015quantum}. As a first application, we see immediately the existence of Hall polynomials for cyclic quivers, a fact established in \\cite{Guo1995hallpoly} and \\cite{Ringel1993composition}, and derive a recursive formula to compute them. We will further use the formula and the construction of certain monomial base for ${\\mathfrak H}_\\Delta(n)$ given in \\cite{DengDuXiao2007generic}, together with the double Ringe"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.01423","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"}