{"paper":{"title":"Lowest Weight Representations, Singular Vectors and Invariant Equations for a Class of Conformal Galilei Algebras","license":"http://creativecommons.org/licenses/by-nc-sa/3.0/","headline":"","cross_cats":["math.MP"],"primary_cat":"math-ph","authors_text":"Jambulingam Segar, Naruhiko Aizawa, Radhakrishnan Chandrashekar","submitted_at":"2014-08-20T23:54:06Z","abstract_excerpt":"The conformal Galilei algebra (CGA) is a non-semisimple Lie algebra labelled by two parameters $d$ and $\\ell$. The aim of the present work is to investigate the lowest weight representations of CGA with $d = 1$ for any integer value of $\\ell$. First we focus on the reducibility of the Verma modules. We give a formula for the Shapovalov determinant and it follows that the Verma module is irreducible if $\\ell = 1$ and the lowest weight is nonvanishing. We prove that the Verma modules contain many singular vectors, i.e., they are reducible when $\\ell \\neq 1$. Using the singular vectors, hierarchi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1408.4842","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"}