### 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 L^{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].

Original language | English (US) |
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Pages (from-to) | 511-529 |

Number of pages | 19 |

Journal | Inventiones Mathematicae |

Volume | 113 |

Issue number | 1 |

DOIs | |

State | Published - Dec 1993 |

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### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

*Inventiones Mathematicae*,

*113*(1), 511-529. https://doi.org/10.1007/BF01244316

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

Research output: Contribution to journal › Article

*Inventiones Mathematicae*, vol. 113, no. 1, pp. 511-529. https://doi.org/10.1007/BF01244316

}

TY - JOUR

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

AU - Bloch, A. M.

AU - Flaschka, Hermann

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

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

U2 - 10.1007/BF01244316

DO - 10.1007/BF01244316

M3 - Article

AN - SCOPUS:0000658384

VL - 113

SP - 511

EP - 529

JO - Inventiones Mathematicae

JF - Inventiones Mathematicae

SN - 0020-9910

IS - 1

ER -