
Journal of Lie Theory 31 (2021), No. 1, 249264 Copyright Heldermann Verlag 2021 Spectra of the RaritaSchwinger Operator on Some Symmetric Spaces Yasushi Homma Dept. of Mathematics, Faculty of Science and Engineering, Waseda University, Tokyo 1698555, Japan homma_yasushi@waseda.jp Takuma Tomihisa Dept. of Pure and Applied Mathematics, Graduate School of Fundamental Science and Engineering, Waseda University, Tokyo 1698555, Japan takutomihisa@akane.waseda.jp We give a method to calculate spectra of the square of the RaritaSchwinger 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, RaritaSchwinger operator, Casimir operator on symmetric spaces. MSC: 53C27, 53C35, 58C40. [ Fulltextpdf (137 KB)] for subscribers only. 