{"paper":{"title":"Representation of the Quantum Plane, its Quantum Double and Harmonic Analysis on $GL_q^+(2,R)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.QA","authors_text":"Ivan Chi-Ho Ip","submitted_at":"2011-08-26T18:28:35Z","abstract_excerpt":"We give complete detail of the description of the GNS representation of the quantum plane $\\cA$ and its dual $\\hat{\\cA}$ as a von-Neumann algebra. In particular we obtain a rather surprising result that the multiplicative unitary $W$ is manageable in this quantum semigroup context. We study the quantum double group construction introduced by Woronowicz, and using Baaj and Vaes' construction of the multiplicative unitary $\\bW_m$, we give the GNS description of the quantum double $\\cD(\\cA)$ which is equivalent to $GL_q^+(2,\\R)$. Furthermore we study the fundamental corepresentation $T^{\\l,t}$ an"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1108.5365","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":""},"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"}