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Article: On The T-leaves Of Some Poisson Structures Related To Products Of Flag Varieties

TitleOn The T-leaves Of Some Poisson Structures Related To Products Of Flag Varieties
Authors
KeywordsPoisson geometry
Flag varieties
T-leaves
Generalized Bruhat cells
Issue Date2017
PublisherAcademic Press. The Journal's web site is located at http://www.elsevier.com/locate/aim
Citation
Advances in Mathematics, 2017, v. 306, p. 1209-1261 How to Cite?
AbstractFor a connected abelian Lie group acting on a Poisson manifold by Poisson isomorphisms, the -leaves of π in Y are the orbits of the symplectic leaves of π under , and the leaf stabilizer of a -leaf is the subspace of the Lie algebra of that is everywhere tangent to all the symplectic leaves in the -leaf. In this paper, we first develop a general theory on -leaves and leaf stabilizers for a class of Poisson structures defined by Lie bialgebra actions and quasitriangular r-matrices. We then apply the general theory to four series of holomorphic Poisson structures on products of flag varieties and related spaces for a complex semi-simple Lie group G. We describe their T-leaf decompositions, where T is a maximal torus of G, in terms of (open) generalized Richardson varieties and generalized double Bruhat cells associated to conjugacy classes of G, and we compute their leaf stabilizers and the dimension of the symplectic leaves in each T-leaf.
DescriptionLink to Open Archive
Persistent Identifierhttp://hdl.handle.net/10722/294084
ISSN
2019 Impact Factor: 1.494
2015 SCImago Journal Rankings: 3.261

 

DC FieldValueLanguage
dc.contributor.authorLu, JH-
dc.contributor.authorMOUQUIN, V-
dc.date.accessioned2020-11-23T08:26:06Z-
dc.date.available2020-11-23T08:26:06Z-
dc.date.issued2017-
dc.identifier.citationAdvances in Mathematics, 2017, v. 306, p. 1209-1261-
dc.identifier.issn0001-8708-
dc.identifier.urihttp://hdl.handle.net/10722/294084-
dc.descriptionLink to Open Archive-
dc.description.abstractFor a connected abelian Lie group acting on a Poisson manifold by Poisson isomorphisms, the -leaves of π in Y are the orbits of the symplectic leaves of π under , and the leaf stabilizer of a -leaf is the subspace of the Lie algebra of that is everywhere tangent to all the symplectic leaves in the -leaf. In this paper, we first develop a general theory on -leaves and leaf stabilizers for a class of Poisson structures defined by Lie bialgebra actions and quasitriangular r-matrices. We then apply the general theory to four series of holomorphic Poisson structures on products of flag varieties and related spaces for a complex semi-simple Lie group G. We describe their T-leaf decompositions, where T is a maximal torus of G, in terms of (open) generalized Richardson varieties and generalized double Bruhat cells associated to conjugacy classes of G, and we compute their leaf stabilizers and the dimension of the symplectic leaves in each T-leaf.-
dc.languageeng-
dc.publisherAcademic Press. The Journal's web site is located at http://www.elsevier.com/locate/aim-
dc.relation.ispartofAdvances in Mathematics-
dc.subjectPoisson geometry-
dc.subjectFlag varieties-
dc.subjectT-leaves-
dc.subjectGeneralized Bruhat cells-
dc.titleOn The T-leaves Of Some Poisson Structures Related To Products Of Flag Varieties-
dc.typeArticle-
dc.identifier.emailLu, JH: jhluhku@hku.hk-
dc.identifier.authorityLu, JH=rp00753-
dc.description.naturelink_to_subscribed_fulltext-
dc.identifier.doi10.1016/j.aim.2016.11.008-
dc.identifier.scopuseid_2-s2.0-84995545949-
dc.identifier.hkuros319318-
dc.identifier.volume306-
dc.identifier.spage1209-
dc.identifier.epage1261-
dc.publisher.placeUnited Kingdom-

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