We develop a graphical representation of polynomial invariants of unitary
gauge groups, and use it to find the algebraic curve corresponding to a
hyperkahler quotient of a linear space. We apply this method to four
dimensional ALE spaces, and for the A_k, D_k, and E_6 cases, derive the
explicit relation between the deformations of the curves away from the orbifold
limit and the Fayet-Iliopoulos parameters in the corresponding quotient
construction. We work out the orbifold limit of E_7, E_8, and some higher
dimensional examples.Comment: Two typos corrected--Journal version; 23 pages, 13 figures, harvma