{"paper":{"title":"Category ${\\mathcal O}$ and locally analytic representations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.NT"],"primary_cat":"math.RT","authors_text":"Matthias Strauch, Sascha Orlik","submitted_at":"2014-12-17T06:44:44Z","abstract_excerpt":"For a split reductive group $G$ over a finite extension $L$ of ${\\mathbb Q}_p$, and a parabolic subgroup $P \\subset G$ we introduce a category ${\\mathcal O}^P$ which is equipped with a forgetful functor to the parabolic category ${\\mathcal O}^{\\mathfrak p}$ of Bernstein, Gelfand and Gelfand. There is a canonical fully faithful embedding of a subcategory ${\\mathcal O}^{\\mathfrak p}_{\\rm alg}$ of ${\\mathcal O}^{\\mathfrak p}$ into ${\\mathcal O}^P$, which 'splits' the forgetful map. We then introduce functors from the category ${\\mathcal O}^P$ to the category of locally analytic representations, t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.5270","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"}