Titel
A dual pair for the contact group
Autor*in
Cornelia Vizman
Department of Mathematics, West University of Timişoara
Abstract
Generalizing the canonical symplectization of contact manifolds, we construct an infinite dimensional non-linear Stiefel manifold of weighted embeddings into a contact manifold. This space carries a symplectic structure such that the contact group and the group of reparametrizations act in a Hamiltonian fashion with equivariant moment maps, respectively, giving rise to a dual pair, called the EPContact dual pair. Via symplectic reduction, this dual pair provides a conceptual identification of non-linear Grassmannians of weighted submanifolds with certain coadjoint orbits of the contact group. Moreover, the EPContact dual pair gives rise to singular solutions for the geodesic equation on the group of contact diffeomorphisms. For the projectivized cotangent bundle, the EPContact dual pair is closely related to the EPDiff dual pair due to Holm and Marsden.
Stichwort
Contact manifoldContact diffeomorphism groupCoadjoint orbitDual pairHomogeneous spaceSymplectic manifoldSymplectizationManifold of mappingsInfinite dimensional manifoldNon-linear GrassmannianNon-linear Stiefel manifold
Objekt-Typ
Sprache
Englisch [eng]
Persistent identifier
https://phaidra.univie.ac.at/o:1628644
Erschienen in
Titel
Mathematische Zeitschrift
Band
301
Ausgabe
3
ISSN
0025-5874
Erscheinungsdatum
2022
Seitenanfang
2937
Seitenende
2973
Verlag
Springer Science and Business Media LLC
Projektnummer
P31663-N35 – Austrian Science Fund (FWF)
Projektnummer
Y963-N35 – Austrian Science Fund (FWF)
Erscheinungsdatum
2022
Zugänglichkeit
Rechteangabe
© The Author(s) 2022

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