Some Operators Associated to Rarita-Schwinger Type Operators

2011/06/17 by Junxia Li, John Ryan, Li, Junxia +1
Mathematics · Physics and Astronomy · #Algebraic and Geometric Analysis #Complex Variables (math.CV) #FOS: Mathematics #Mathematical functions and polynomials #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.1106.3588

openalex publication_date 2011/06/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we study some operators associated to the Rarita-Schwinger operators. They arise from the difference between the Dirac operator and the Rarita-Schwinger operators. These operators are called remaining operators. They are based on the Dirac operator and projection operators I-P_k. The fundamental solutions of these operators are harmonic polynomials, homogeneous of degree k. First we study the remaining operators and their representation theory in Euclidean space. Second, we can extend the remaining operators in Euclidean space to the sphere under the Cayley transformation.

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