{"paper":{"title":"The $\\ct$ transform on line bundles over compact Hermitian symmetric spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.RT","authors_text":"Gestur Olafsson, Vivian M. Ho","submitted_at":"2015-12-01T00:54:02Z","abstract_excerpt":"In a previous article the second author together with A. Pasquale determined the spectrum of the $Cos^\\lambda$ transform on smooth functions on the Grassmann manifolds $G_{p,n+1}$. This article extends those results to line bundles over certain Grassmannians. In particular we define the $Cos^\\lambda$ transform on smooth sections of homogeneous line bundles over$G_{p,n+1}$ and show that it is an intertwining operator between generalized ($\\chi$-spherical) principal series representations induced from a maximal parabolic subgroup of $\\mathrm{SL} (n+1, \\mathbb{K})$. Then we use the spectrum gener"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1512.00110","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"}