Summary
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 toL 2 ([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].
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Dedicated to Professor Takeshi Kotake on the occasion of his 60th birthday
Oblatum 25-XI-1992 & 17-III-1993
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Bloch, A.M., Flaschka, H. & Ratiu, T. A Schur-Horn-Kostant convexity theorem for the diffeomorphism group of the annulus. Invent Math 113, 511–529 (1993). https://doi.org/10.1007/BF01244316
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DOI: https://doi.org/10.1007/BF01244316