Journal of Lie Theory

no. 1
Spectra of the Rarita-Schwinger Operator on Some Symmetric Spaces
Journal of Lie Theory, Volume 31 (2021) no. 1, pp. 249-264
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.
DOI: 10.5802/jolt.1169
Classification: 53C27, 53C35, 58C40
Keywords: Dirac operator, Rarita-Schwinger operator, Casimir operator on symmetric spaces 
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     author = {Y. Homma and T. Tomihisa},
     title = {Spectra of the {Rarita-Schwinger} {Operator} on {Some} {Symmetric} {Spaces}},
     journal = {Journal of Lie Theory},
     pages = {249--264},
     year = {2021},
     volume = {31},
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     doi = {10.5802/jolt.1169},
     zbl = {1464.53065},
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Y. Homma; T. Tomihisa. Spectra of the Rarita-Schwinger Operator on Some Symmetric Spaces. Journal of Lie Theory, Volume 31 (2021) no. 1, pp. 249-264. doi: 10.5802/jolt.1169

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