Spectra of the rarita-schwinger operator on some symmetric spaces

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Abstract

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.

Original languageEnglish
Pages (from-to)249-264
Number of pages16
JournalJournal of Lie Theory
Volume31
Issue number1
Publication statusPublished - 2021

Keywords

  • Casimir operator on symmetric spaces
  • Dirac operator
  • Rarita-Schwinger operator

ASJC Scopus subject areas

  • Algebra and Number Theory

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