{"paper":{"title":"On distinguished orbits of reductive representations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DG"],"primary_cat":"math.RT","authors_text":"Edison Alberto Fern\\'andez-Culma","submitted_at":"2013-01-21T18:31:23Z","abstract_excerpt":"Let $G$ be a real reductive Lie group and ${\\tau}:G \\longrightarrow GL(V)$ be a real reductive representation of $G$ with (restricted) moment map $m_{\\ggo}: V-{0} \\longrightarrow \\ggo$. In this work, we introduce the notion of \"nice space\" of a real reductive representation to study the problem of how to determine if a $G$-orbit is \"distinguished\" (i.e. it contains a critical point of the norm squared of $m_{\\ggo}$). We give an elementary proof of the well-known convexity theorem of Atiyah-Guillemin-Sternberg in our particular case and we use it to give an easy-to-check sufficient condition fo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1301.4949","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"}