Spectra of the Rarita-Schwinger operator on some symmetric spaces

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.

The spinor and tensor fields with higher spin on spaces of constant curvature

“…To clarify the meaning of the factorization, we show how the spinor fields with spin j + 1/2 are influenced by the spinor fields with lower spin in Theorem 7. Remark that, for the case of j = 1, we need only the assumption of Einstein manifold and can develop fruitful geometry and analysis in [1], [18] and [19]. Next, we study harmonic analysis on spinor fields with spin j +1/2 on the standard sphere as a model case for spinor analysis on a curved space in Section 3.…”