  We give a positive answer to the Berry-Robbins problem for any compact Lie
group G, i.e. we show the existence of a smooth W-equivariant map from the
space of regular triples in a Cartan subalgebra to the flag manifold G/T. This
map is constructed via solutions to Nahm's equations and it is compatible with
the SO(3) action, where SO(3) acts on G/T via a regular homomorphism from SU(2)
to G. We then generalize this picture to include an arbitrary homomorphism from
SU(2) to G. This leads to an interesting geometrical picture which appears to
be related to the Springer representation of the Weyl group and the work of
Kazhdan and Lusztig on representations of Hecke algebras.
