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

A. M. Bloch, Hermann Flaschka, T. Ratiu

Research output: Contribution to journalArticle

9 Citations (Scopus)

Abstract

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].

Original languageEnglish (US)
Pages (from-to)511-529
Number of pages19
JournalInventiones Mathematicae
Volume113
Issue number1
DOIs
StatePublished - Dec 1993

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Diffeomorphism Group
Ring or annulus
Convexity
Diffeomorphisms
Orbit
Theorem
Cartan Subalgebra
Measure-preserving Transformations
Compact Convex Set
Unitary Operator
Extreme Points
Completion
Lie Algebra
Permutation
Semigroup
Isomorphic
Hilbert space
Projection

ASJC Scopus subject areas

  • Mathematics(all)

Cite this

A Schur-Horn-Kostant convexity theorem for the diffeomorphism group of the annulus. / Bloch, A. M.; Flaschka, Hermann; Ratiu, T.

In: Inventiones Mathematicae, Vol. 113, No. 1, 12.1993, p. 511-529.

Research output: Contribution to journalArticle

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