{"paper":{"title":"Split Quaternionic Analysis and Separation of the Series for SL(2,R) and SL(2,C)/SL(2,R)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CV"],"primary_cat":"math.RT","authors_text":"Igor Frenkel, Matvei Libine","submitted_at":"2010-09-13T22:31:23Z","abstract_excerpt":"We extend our previous study of quaternionic analysis based on representation theory to the case of split quaternions H_R. The special role of the unit sphere in the classical quaternions H identified with the group SU(2) is now played by the group SL(2,R) realized by the unit quaternions in H_R. As in the previous work, we use an analogue of the Cayley transform to relate the analysis on SL(2,R) to the analysis on the imaginary Lobachevski space SL(2,C)/SL(2,R) identified with the one-sheeted hyperboloid in the Minkowski space M. We study the counterparts of Cauchy-Fueter and Poisson formulas"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1009.2532","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"}