Conjecture on homogeneous and real analytic Poisson vector bundles

Let ${\mathfrak g}$ be a semisimple Lie algebra of non-compact type, and let $G$ be the corresponding Lie group. A Poisson vector bundle is a vector bundle equipped with a compatible Poisson structure; it is homogeneous when it has the homogeneity property considered in the paper, and Poisson-trivial when it is trivial in the Poisson category.

Poisson vector bundle conjecture. (1) Every homogeneous Hermitian Poisson vector bundle over ${\mathfrak g}^*$ is Poisson-trivial. (2) There is a one-to-one correspondence between germs of real analytic Poisson vector bundles over ${\mathfrak g}^*$ and representations of $G$.

The first assertion would provide the expected analogue of the compact classification result, while the second predicts a classification of real analytic Poisson vector bundles by representation-theoretic data. The supplied text does not state whether either assertion has been resolved.