Thursday, March 14, 2013

1303.3167 (Indranil Biswas et al.)

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

Indranil Biswas, Avijit Mukherjee
In this continuation of \cite{BM}, we prove the following: Let $\Gamma\subset \text{SL}(2,{\mathbb C})$ be a cocompact lattice, and let $\rho: \Gamma \rightarrow \text{GL}(r,{\mathbb C})$ be an irreducible representation. Then the holomorphic vector bundle $E_\rho \longrightarrow \text{SL}(2,{\mathbb C})/\Gamma$ 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.
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