{"paper":{"title":"On some families of smooth affine spherical varieties of full rank","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.RT","math.SG"],"primary_cat":"math.AG","authors_text":"Bart Van Steirteghem, Guido Pezzini, Kay Paulus","submitted_at":"2017-05-15T17:51:09Z","abstract_excerpt":"Let G be a complex connected reductive group. I. Losev has shown that a smooth affine spherical G-variety X is uniquely determined by its weight monoid, which is the set of irreducible representations of G that occur in the coordinate ring of X. In this paper we use a combinatorial characterization of the weight monoids of smooth affine spherical varieties to classify: (a) all such varieties when G is $\\mathrm{SL}(2) \\times \\mathbb{C}^{\\times}$ and (b) all such varieties for G simple which have a G-saturated weight monoid of full rank. We also use the characterization and F. Knop's classificat"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.05357","kind":"arxiv","version":2},"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"}