{"paper":{"title":"On Conjugation orbits of semisimple pairs in rank one","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GT","authors_text":"Krishnendu Gongopadhyay, Sagar B. Kalane","submitted_at":"2018-01-18T14:18:35Z","abstract_excerpt":"We consider Lie groups ${\\rm SU}(n,1)$ and ${\\rm Sp}(n,1)$ that act as the isometries of the complex and quaternionic hyperbolic spaces respectively. We classify pairs of semisimple elements in ${\\rm Sp}(n,1)$ and ${\\rm SU}(n,1)$ up to conjugacy. This gives local parametrization of the representations $\\rho$ in $Hom(F_2, G)/G$ such that both $\\rho(x)$ and $\\rho(y)$ are hyperbolics, where $F_2=\\langle x, y\\rangle$, $G={\\rm Sp}(n,1)$ or ${\\rm SU}(n,1)$. We use the ${\\rm PSp}(n,1)$-configuration space $M(n,i,m-i)$ of ordered $m$-tuples of points on $\\overline{{\\bf H}_{\\mathbb H}^n}$, where first "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1801.06431","kind":"arxiv","version":6},"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"}