A SCHUR-HORN-KOSTANT CONVEXITY THEOREM FOR THE DIFFEOMORPHISM GROUP OF THE ANNULUS

The group of area preserving diffeomorphisms of the annulus acts on it s Lie algebra, the globally Hamiltonian vectorfields on the annulus. W e consider a certain Hilbert space completion of this group (thinking of it as a group of unitary operators induced by the diffeomorphisms), and prove that the projection of an adjoint orbit onto a ''Cartan'' s ubalgebra isomorphic to L2([0, 1]) is an infinite-dimensional, weakly compact, convex set, whose extreme points coincide with the orbit, thr ough a certain function, of the ''permutation'' semigroup of measure p reserving transformations of [0, 1].