Geodesic
Spectra of the Rarita-Schwinger Operator on Some Symmetric Spaces
Yasushi Homma1 ; Takuma Tomihisa2
1Dept. of Mathematics, Faculty of Science and Engineering, Waseda University, Tokyo 169-8555, Japan
2Dept. of Pure and Applied Mathematics, Graduate School of Fundamental Science and Engineering, Waseda University, Tokyo 169-8555, Japan
Journal of Lie Theory, Tome 31 (2021) no. 1, pp. 249-264

Voir la notice de l'article provenant de la source Heldermann Verlag

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.
Classification : 53C27, 53C35, 58C40
Mots-clés : Dirac operator, Rarita-Schwinger operator, Casimir operator on symmetric spaces

Yasushi Homma  1   ; Takuma Tomihisa  2

1 Dept. of Mathematics, Faculty of Science and Engineering, Waseda University, Tokyo 169-8555, Japan
2 Dept. of Pure and Applied Mathematics, Graduate School of Fundamental Science and Engineering, Waseda University, Tokyo 169-8555, Japan 
Yasushi Homma; Takuma Tomihisa. Spectra of the Rarita-Schwinger Operator on Some Symmetric Spaces. Journal of Lie Theory, Tome 31 (2021) no. 1, pp. 249-264. http://geodesic.mathdoc.fr/item/JOLT_2021_31_1_a13/
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