Differential symmetry breaking operators from a line bundle to a vector bundle over real projective spaces

2024/08/02 by Kubo, Toshihisa
#17B10 #22E46 #Differential Geometry (math.DG) #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2408.01213

Abstract

In this paper we classify and construct differential symmetry breaking operators \mathbbD from a line bundle over the real projective space ℝℙⁿ to a vector bundle over ℝℙ^n-1. We further determine the factorization identities of \mathbbD and the branching laws of the corresponding generalized Verma modules of \mathfraksl(n+1,ℂ). By utilizing the factorization identities, the SL(n,ℝ)-representations realized on the image Im(\mathbbD) are also investigated.

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