Journal of Lie Theory 31 (2021), No. 1, 249--264
Copyright Heldermann Verlag 2021
Spectra of the Rarita-Schwinger Operator on Some Symmetric Spaces
Yasushi Homma
Dept. of Mathematics, Faculty of Science and Engineering, Waseda University, Tokyo 169-8555, Japan
homma_yasushi@waseda.jp
Takuma Tomihisa
Dept. of Pure and Applied Mathematics, Graduate School of Fundamental Science and Engineering, Waseda University, Tokyo 169-8555, Japan
taku-tomihisa@akane.waseda.jp
We give a method to calculate spectra of the square of the Rarita-Schwinger operator on compact symmetric spaces. According to Weitzenböck's 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.
Keywords: Dirac operator, Rarita-Schwinger operator, Casimir operator on symmetric spaces.
MSC: 53C27, 53C35, 58C40.
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