If G is a compact Lie group, the moduli space of orbits of the coadjoint action of G on g∗ (the dual of the Lie algebra) is given by h/W where h is a Cartan subalgebra of g and W is the Weyl group (for SU(N), it is simply saying that up to conjugation by SU(N), an antihermitian matrix is characterized by its eigenvalues up to permutation).
Gorsky and Nekasov consider an infinite dimensional version of this story, replacing G by the loop group of G, i.e. the group of maps from the circle to G. The moduli space of the orbits becomes the space of maps from the circle to h/W.