Existence of nearly holomorphic sections on compact Hermitian symmetric\n spaces

2013/03/11 by Benjamin Schwarz, Schwarz, Benjamin
Mathematics · Physics and Astronomy · #17C50 (Secondary) #22E46 #32A50 #32L10 #32M15 (Primary) 32D15 #Advanced Algebra and Geometry #Advanced Differential Geometry Research #Complex Variables (math.CV) #FOS: Mathematics #Geometry and complex manifolds #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1303.2680

openalex publication_date 2013/03/11 · openalex created_date 2025/10/24 · openalex updated_date 2026/07/28

Abstract

Let X=U/K be a compact Hermitian symmetric space, and let sE be a\nU-homogeneous Hermitian vector bundle on X. In a previous paper, we showed\nthat the space of nearly holomorphic sections is well-adapted for harmonic\nanalysis in L²(X, sE) provided that non-trivial nearly holomorphic sections\ndo exist. Here we investigate the problem of extending local nearly holomorphic\nsections to global ones and prove the existence of non-trivial nearly\nholomorphic sections. This extends the results on the U-type decomposition of\nL²(X, sE) from our previous paper.\n

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