TY - JOUR

T1 - A Schur-Horn-Kostant convexity theorem for the diffeomorphism group of the annulus

AU - Bloch, A. M.

AU - Flaschka, H.

AU - Ratiu, T.

PY - 1993/12

Y1 - 1993/12

N2 - The group of area preserving diffeomorphisms of the annulus acts on its Lie algebra, the globally Hamiltonian vectorfields on the annulus. We 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" subalgebra isomorphic to L2 ([0, 1]) is an infinite-dimensional, weakly compact, convex set, whose extreme points coincide with the orbit, through a certain function, of the "permutation" semigroup of measure preserving transformations of [0, 1].

AB - The group of area preserving diffeomorphisms of the annulus acts on its Lie algebra, the globally Hamiltonian vectorfields on the annulus. We 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" subalgebra isomorphic to L2 ([0, 1]) is an infinite-dimensional, weakly compact, convex set, whose extreme points coincide with the orbit, through a certain function, of the "permutation" semigroup of measure preserving transformations of [0, 1].

UR - http://www.scopus.com/inward/record.url?scp=0000658384&partnerID=8YFLogxK

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U2 - 10.1007/BF01244316

DO - 10.1007/BF01244316

M3 - Article

AN - SCOPUS:0000658384

SN - 0020-9910

VL - 113

SP - 511

EP - 529

JO - Inventiones Mathematicae

JF - Inventiones Mathematicae

IS - 1

ER -