Am. Bloch et al., A SCHUR-HORN-KOSTANT CONVEXITY THEOREM FOR THE DIFFEOMORPHISM GROUP OF THE ANNULUS, Inventiones Mathematicae, 113(3), 1993, pp. 511-529
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].