Equivariant differential operators on spinors in conformal geometry

2016/02/03 by Křižka, Libor, Somberg, Petr
#15A66 #20G05 #53A30 #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.1602.01403

Abstract

We present a novel approach to the classification of conformally equivariant differential operators on spinors in the case of homogeneous conformal geometry. It is based on the classification of solutions for a vector-valued system of partial differential equations, associated to D-modules for the homogeneous conformal structure and controlled by the spin Howe duality for the orthogonal Lie algebras.

Related

• Construction of Arbitrary Order Conformally Invariant Operators in Higher Spin Spaces
• On Conformal Powers of the Dirac Operator on Spin Manifolds
• Methods of Equivariant Quantization
• Non-linear partial differential equations in conformal geometry
• Conformally equivariant quantization: Existence and uniqueness