The \ct transform on line bundles over compact Hermitian symmetric spaces

2015/12/01 by Vivian M. Ho, Ho, Vivian M., Gestur Ólafsson +1
Mathematics · #22E46 #43A80 #44A15 #53C35 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometry and complex manifolds #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1512.00110

openalex publication_date 2015/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

In a previous article the second author together with A. Pasquale determined the spectrum of the Cos^λ 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^λ transform on smooth sections of homogeneous line bundles overG_p,n+1 and show that it is an intertwining operator between generalized (χ-spherical) principal series representations induced from a maximal parabolic subgroup of SL (n+1, \mathbbK). Then we use the spectrum generating method to determine the K-spectrum of the Cos^λ transform.

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