Title: Polynomiality for the Poisson centre of truncated maximal parabolic subalgebras,
Abstract: We show that the Poisson centre of truncated maximal parabolic subalgebras of
a simple Lie algebra of type B, D and E_6 is a polynomial algebra.
In roughly half of the cases the polynomiality of the Poisson centre was
already known by a completely different method.
For the rest of the cases, our approach is to construct an algebraic slice in
the sense of Kostant given by an adapted pair and the computation of an
improved upper bound for the Poisson centre.