Finite-dimensional coadjoint orbits in loop algebras

We give a classification of the finite dimensional coadjoint orbits in the dual of the algebra₊ of polynomials in one variable with values in a semi-simple Lie algebra, and generalise this result to algebras defined over an arbitrary Riemann surface.During the preparation of this work the author was supported by NSERC grant A8361 and FCAR grant EQ3518.