{"paper":{"title":"Simple weak modules for the fixed point subalgebra of the Heisenberg vertex operator algebra of rank $1$ by an automorphism of order $2$ and Whittaker vectors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.QA","authors_text":"Kenichiro Tanabe","submitted_at":"2016-08-29T02:10:34Z","abstract_excerpt":"Let $M(1)$ be the vertex operator algebra with the Virasoro element $\\omega$ associated to the Heisenberg algebra of rank $1$ and let $M(1)^{+}$ be the subalgebra of $M(1)$ consisting of the fixed points of an automorphism of $M(1)$ of order $2$. We classify the simple weak $M(1)^{+}$-modules with a non-zero element $w$ such that for some integer $s\\geq 2$, $\\omega_i w\\in{\\mathbb C}w$ ($i=\\lfloor s/2\\rfloor+1,\\lfloor s/2\\rfloor+2,\\ldots,s-1$), $\\omega_{s}w\\in{\\mathbb C}^{\\times}w$, and $\\omega_i w=0$ for all $i>s$. The result says that any such simple weak $M(1)^{+}$-module is isomorphic to so"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1608.07890","kind":"arxiv","version":3},"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"}