Translation of harmonic spinors and interacting Weyl fermions on homogeneous spaces (Q1625131)

In the paper [Dev. Math. 37, 161--181 (2014; Zbl 1319.22010)], \textit{S. Mehdi} and \textit{R. Zierau} defined a Poisson map intertwining a principal series representation with a submodule in the kernel of the Dirac operator which, in the language of quantum dynamics, corresponds to Weyl fermions. In this paper, the authors show that the above Poisson map commutes with the translation functor. As a result, the authors give a representation theoretic approach of `translating' a Weyl fermion on a twisted spin bundle to another Weyl fermion on another twisted spin bundle for a fixed homogeneous space. For the entire collection see [Zbl 1392.42001].