Spectra of the Rarita-Schwinger operator on some symmetric spaces

2020/01/17 by Yasushi Homma, Homma, Yasushi, Takuma Tomihisa +1
Physics and Astronomy · Mathematics · #Advanced Differential Geometry Research #Algebraic and Geometric Analysis #Advanced Topics in Algebra

paper · pdf · doi:10.48550/arxiv.2001.06167

Abstract

We give a method to calculate spectra of the square of the Rarita-Schwinger operator on compact symmetric spaces. According to Weitzenböck formulas, the operator can be written by the Laplace operator, which is the Casimir operator on compact symmetric spaces. Then we can obtain the spectra by using the Freudenthal's formula and branching rules. As examples, we calculate the spectra on the sphere, the complex projective space, and the quaternionic projective space.

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