{"paper":{"title":"Archimedean superrigidity of solvable S-arithmetic groups","license":"","headline":"","cross_cats":["math.NT"],"primary_cat":"math.RT","authors_text":"Dave Witte","submitted_at":"1996-11-19T00:00:00Z","abstract_excerpt":"Let $\\Ga$ be a connected, solvable linear algebraic group over a number field~$K$, let $S$ be a finite set of places of~$K$ that contains all the infinite places, and let $\\theints$ be the ring of $S$-integers of~$K$. We define a certain closed subgroup~$\\GOS$ of $\\Ga_S = \\prod_{v \\in S} \\Ga_{K_v}$ that contains $\\Ga_{\\theints}$, and prove that $\\Ga_{\\theints}$ is a superrigid lattice in~$\\GOS$, by which we mean that finite-dimensional representations $\\alpha\\colon \\Ga_{\\theints} \\to \\GL_n(\\real)$ more-or-less extend to representations of~$\\GOS$.\n  The subgroup~$\\GOS$ may be a proper subgroup "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9611219","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"}