  We point out, and draw some consequences of, the fact that the Poisson Lie
group G* dual to G=GL_n(C) (with its standard complex Poisson structure) may be
identified with a certain moduli space of meromorphic connections on the unit
disc having an irregular singularity at the origin. The Riemann-Hilbert map for
such connections, taking the Stokes data, induces a holomorphic map from the
dual of the Lie algebra of G to the Poisson Lie group G*. The main result is
that this map is Poisson.
  First this leads to new, more direct, proofs of theorems of Duistermaat and
Ginzburg-Weinstein (enabling one to reduce Kostant's non-linear convexity
theorem, involving the Iwasawa projection, to the linear convexity theorem,
involving the `diagonal part').
  Secondly we obtain a new approach to the braid group invariant Poisson
structure on Dubrovin's local moduli space of semisimple Frobenius manifolds:
it is induced from the standard Poisson structure on G*.
