TY - JOUR

T1 - Spectra of the rarita-schwinger operator on some symmetric spaces

AU - Homma, Yasushi

AU - Tomihisa, Takuma

N1 - Funding Information:
Acknowledgements. This research was partially supported by JSPS KAKENHI Grant Number JP19K03480.
Publisher Copyright:
© 2021 Heldermann Verlag.

PY - 2021

Y1 - 2021

N2 - 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.

AB - 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.

KW - Casimir operator on symmetric spaces

KW - Dirac operator

KW - Rarita-Schwinger operator

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M3 - Article

AN - SCOPUS:85104801452

VL - 31

SP - 249

EP - 264

JO - Journal of Lie Theory

JF - Journal of Lie Theory

SN - 0949-5932

IS - 1

ER -