  We consider string junctions with endpoints on a set of branes of IIB string
theory defining an ADE-type gauge Lie algebra. We show how to characterize
uniquely equivalence classes of junctions related by string/brane crossing
through invariant charges that count the effective number of prongs ending on
each brane. Each equivalence class defines a point on a lattice of junctions.
We define a metric on this lattice arising from the intersection pairing of
junctions, and use self-intersection to identify junctions in the adjoint and
fundamental representations of all ADE algebras. This information suffices to
determine the relation between junction lattices and the Lie-algebra weight
lattices. Arbitrary representations are built by allowing junctions with
asymptotic (p,q) charges, on which the group of conjugacy classes of
representations is represented additively. One can view the (p,q) asymptotic
charges as Dynkin labels associated to two new fundamental weight vectors.
