Translation of harmonic spinors and interacting weyl fermions on homogeneous spaces

Salah Mehdi (1) , Nicolas Prudhon (1)

1 IECL - Institut Élie Cartan de Lorraine

We show that the image of the Poisson map, defined by Mehdi and Zierau in [MZ14b], which intertwines principal series representations with a submodule of the kernel of the cubic Dirac operator, commutes with the translation functor. As a byproduct, we obtain a systematic geometric process which produces interacting Weyl fermions with a fixed energy level on homogeneous spacetimes.

Mots clés: Dirac operator; harmonic spinor; homogeneous space; admissible representation; translation functor; Weyl fermion; interaction

Domaines: Mathématiques [math]

Salah Mehdi, Nicolas Prudhon. Translation of harmonic spinors and interacting weyl fermions on homogeneous spaces. Salah Mehdi; Nicolas Prudhon. TJC 2015 : Geometric and Harmonic Analysis on Homogeneous Spaces and Applications, 207, Springer, pp.185-208, 2018, Springer Proceedings in Mathematics & Statistics (PROMS), 978-3-319-65180-4. ⟨10.1007/978-3-319-65181-1_7⟩. ⟨hal-03336288⟩