{"paper":{"title":"Finite Singular Orbit Modules for Algebraic Groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GR","authors_text":"Aluna Rizzoli","submitted_at":"2019-07-15T21:06:43Z","abstract_excerpt":"Building on the classification of modules for algebraic groups with finitely many orbits on subspaces, we determine all faithful irreducible modules for simple and maximal-semisimple connected algebraic groups that are orthogonal and have finitely many orbits on singular $1$-spaces. This question is naturally connected with the problem of finding for which pairs of subgroups $H,K$ of an algebraic group $G$ there are finitely many $(H,K)$-double cosets. This paper provides a solution to the question when $K$ is a maximal parabolic subgroup $P_1$ of a classical group $SO_n$. We find an interesti"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1907.06755","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"}