{"paper":{"title":"$\\W_n^+$- and $W_n$-module structures on $U(h)$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.QA"],"primary_cat":"math.RT","authors_text":"Haijun Tan, Kaiming Zhao","submitted_at":"2014-01-06T15:44:33Z","abstract_excerpt":"Let $\\h_n$ be the Cartan subalgebra of the Witt algebras $\\W_n^+=\\text{Der}\\C[t_1, t_2, ..., t_n]$ and $\\W_n=\\text{Der}\\C[t_1^{\\pm 1},t_2^{\\pm 1},\\cdots,t_n^{\\pm1}]$ where $1\\le n\\le \\infty$. In this paper, we classify the modules over $\\W_n^+$ and over $\\W_n$ which are free $U(\\h_n)$-modules of rank $1$. These are the $\\W_n^+$-modules $\\Omega(\\Lambda_{n},a, S) $ for some $\\Lambda_n=(\\lambda_1,\\cdots,\\lambda_n) \\in (\\C^*)^n, a\\in \\C$, and $S\\subset \\{1,2,..., n\\}$; and $\\W_n$-modules $\\Omega(\\Lambda_n,a)$ for some $\\Lambda_n\\in (\\C^*)^n$ and some $a\\in \\C.$"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1401.1120","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"}