{"paper":{"title":"The $Cos^\\lambda$ and $Sin^\\lambda$ Transforms as Intertwining Operators between generalized principal series Representations of SL (n+1,K)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Angela Pasquale, Gestur Olafsson","submitted_at":"2011-03-23T15:45:44Z","abstract_excerpt":"In this article we connect topics from convex and integral geometry with well known topics in representation theory of semisimple Lie groups by showing that the $Cos^\\lamda$ and $Sin^\\lambda$-transforms on the Grassmann manifolds $Gr_p(K)=SU (n+1,K)/S (U (p,K)\\times U (n+1-p,K))$ are standard intertwining operators between certain generalized principal series representations induced from a maximal parabolic subgroup $P_p$ of $SL (n+1,K)$. The index ${}_p$ indicates the dependence of the parabolic on p. The general results of Knapp and Stein and Vogan and Wallach then show that both transforms "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1103.4557","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"}