{"paper":{"title":"Complexity $c$ Pairs in Simple Algebraic Groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT"],"primary_cat":"math.AG","authors_text":"Mahir Bilen Can","submitted_at":"2017-03-15T10:52:03Z","abstract_excerpt":"We call a pair of closed subgroups $(G_1,G_2)$ from a connected reductive algebraic group $G$ a {\\it complexity $c$ pair} if the multiplication action of the pair on $G$ is of complexity $c$. The main focus of this article is on the cases where $G$ is simple and $c$ is either 0 or 1. After showing that both of the subgroups $G_1$ and $G_2$ cannot be reductive subgroups unless $c>1$, we look for the cases where exactly one of the subgroups $G_1$ and $G_2$ is reductive. It turns out that there are only a few such pairs, and their classification involves the horospherical homogeneous spaces of sm"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1703.05076","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"}