On the vector bundles associated to irreducible representations of cocompact lattices of SL(2,C)

Abstract

In this continuation of \cite{BM}, we prove the following: Let $\Gamma \subset \text{SL}(2,\mathbb{C})$ be a cocompact lattice, and let $\rho :\Gamma \to \text{GL}(r,\mathbb{C})$ be an irreducible representation. Then the holomorphic vector bundle $E_{\rho }⟶\text{SL}(2,\mathbb{C})/\Gamma$ associated to $\rho$ is polystable. The compact complex manifold $\text{SL}(2,\mathbb{C})/\Gamma$ has natural Hermitian structures; the polystability of $E_{\rho }$ is with respect to these natural Hermitian structures.

arXiv commentA couple of typos corrected