{"paper":{"title":"Algebraic methods in the theory of generalized Harish-Chandra modules","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Gregg Zuckerman, Ivan Penkov","submitted_at":"2013-10-30T08:08:10Z","abstract_excerpt":"This paper is a review of results on generalized Harish-Chandra modules in the framework of cohomological induction. The main results, obtained during the last 10 years, concern the structure of the fundamental series of $(\\mathfrak{g},\\mathfrak{k})-$modules, where $\\mathfrak{g}$ is a semisimple Lie algebra and $\\mathfrak{k}$ is an arbitrary algebraic reductive in $\\mathfrak{g}$ subalgebra. These results lead to a classification of simple $(\\mathfrak{g},\\mathfrak{k})-$modules of finite type with generic minimal $\\mathfrak{k}-$types, which we state. We establish a new result about the Fernando-"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1310.8058","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"}