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

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

No reviews yet.

No comments yet.