Abstract
Extending earlier results on the duality symmetries of
three-brane probe theories we define the duality subgroup of SL(2,
)
as the symmetry group of the background 7-branes configurations. We
establish that the action of Weyl reflections is implemented on
junctions by brane transpositions that amount to exchanging branes
that can be connected by open strings. This enables us to characterize
duality groups of brane configurations by a map to the symmetry group
of the Dynkin diagram. We compute the duality groups and their
actions for all localizable 7-brane configurations. Surprisingly, for
the case of affine configurations there are brane transpositions
leaving them invariant but acting nontrivially on the charges of
junctions.