{"paper":{"title":"Integral group actions on symmetric spaces and discrete duality symmetries of supergravity theories","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.GR"],"primary_cat":"hep-th","authors_text":"Hisham Sati, Lisa Carbone, Scott H. Murray","submitted_at":"2014-07-12T10:45:48Z","abstract_excerpt":"For $G(\\mathbb{R})$ a split, simply connected, semisimple Lie group of rank $n$ and $K$ the maximal compact subgroup of $G$, we give a method for computing Iwasawa coordinates of $G/K$ using the Chevalley generators and the Steinberg presentation. When $G/K$ is a scalar coset for a supergravity theory in dimensions $\\geq 3$, we determine the action of the integral form $G(\\mathbb{Z})$ on $G/K$. We give explicit results for the action of the discrete $U$--duality groups $SL_2(\\mathbb{Z})$ and $E_7(\\mathbb{Z})$ on the scalar cosets $SL_2(\\mathbb{R})/SO_2(\\mathbb{R})$ and $E_{7(+7)}(\\mathbb{R})/["},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.3370","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"}