{"paper":{"title":"Quasi-Whittaker modules for the Schr\\\"odinger algebra","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math-ph","math.MP"],"primary_cat":"math.RT","authors_text":"Ran Shen, Yan-an Cai, Yongsheng Cheng","submitted_at":"2013-11-19T19:48:05Z","abstract_excerpt":"In this paper, we construct a new class of modules for the Schr\\\"{o}dinger algebra $\\mS$, called quasi-Whittaker module. Different from \\cite{[ZC]}, the quasi-Whittaker module is not induced by the Borel subalgebra of the Schr\\\"{o}dinger algebra related with the triangular decomposition, but its Heisenberg subalgebra $\\mH$. We prove that, for a simple $\\mS$-module $V$, $V$ is a quasi-Whittaker module if and only if $V$ is a locally finite $\\mH$-module; Furthermore, we classify the simple quasi-Whittaker modules by the elements with the action similar to the center elements in $U(\\mS)$ and thei"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.4855","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"}