{"paper":{"title":"Decompositions of Generalized Wavelet Representations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"A. Mayeli, B. Currey, V. Oussa","submitted_at":"2014-01-09T23:21:07Z","abstract_excerpt":"Let $N$ be a simply connected, connected nilpotent Lie group which admits a uniform subgroup $\\Gamma.$ Let $\\alpha$ be an automorphism of $N$ defined by $\\alpha\\left( \\exp X\\right) =\\exp AX.$ We assume that the linear action of $A$ is diagonalizable and we do not assume that $N$ is commutative. Let $W$ be a unitary wavelet representation of the semi-direct product group $\\left\\langle \\cup_{j\\in\\mathbb{Z}}\\alpha^{j}\\left( \\Gamma\\right) \\right\\rangle \\rtimes\\left\\langle \\alpha\\right\\rangle $ defined by $W\\left( \\gamma,1\\right) =f\\left( \\gamma^{-1}x\\right) $ and $W\\left( 1,\\alpha\\right) =\\left\\ve"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.2201","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"}