{"paper":{"title":"Wave Front Sets of Reductive Lie Group Representations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Benjamin Harris, Gestur Olafsson, Hongyu He","submitted_at":"2013-08-08T14:43:05Z","abstract_excerpt":"If $G$ is a Lie group, $H\\subset G$ is a closed subgroup, and $\\tau$ is a unitary representation of $H$, then the authors give a sufficient condition on $\\xi\\in i\\mathfrak{g}^*$ to be in the wave front set of $\\operatorname{Ind}_H^G\\tau$. In the special case where $\\tau$ is the trivial representation, this result was conjectured by Howe. If $G$ is a real, reductive algebraic group and $\\pi$ is a unitary representation of $G$ that is weakly contained in the regular representation, then the authors give a geometric description of $\\operatorname{WF}(\\pi)$ in terms of the direct integral decomposi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1308.1863","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"}