{"paper":{"title":"Positive energy representations for locally finite split Lie algebras","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Karl-Hermann Neeb, Timoth\\'ee Marquis","submitted_at":"2015-07-22T07:04:52Z","abstract_excerpt":"Let $\\mathfrak g$ be a locally finite split simple complex Lie algebra of type $A_J$, $B_J$, $C_J$ or $D_J$ and $\\mathfrak h \\subseteq \\mathfrak g$ be a splitting Cartan subalgebra. Fix $D \\in \\mathrm{der}(\\mathfrak g)$ with $\\mathfrak h \\subseteq \\ker D$ (a diagonal derivation). Then every unitary highest weight representation $(\\rho_\\lambda, V^\\lambda)$ of $\\mathfrak g$ extends to a representation $\\tilde\\rho_\\lambda$ of the semidirect product $\\mathfrak g \\rtimes \\mathbb C D$ and we say that $\\tilde\\rho_\\lambda$ is a positive energy representation if the spectrum of $-i\\tilde\\rho_\\lambda(D)"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1507.06077","kind":"arxiv","version":1},"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"}