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- Publisher Website: 10.1016/j.aim.2016.11.008
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Article: On The T-leaves Of Some Poisson Structures Related To Products Of Flag Varieties
Title | On The T-leaves Of Some Poisson Structures Related To Products Of Flag Varieties |
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Authors | |
Keywords | Poisson geometry Flag varieties T-leaves Generalized Bruhat cells |
Issue Date | 2017 |
Publisher | Academic 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? |
Abstract | For 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. |
Description | Link to Open Archive |
Persistent Identifier | http://hdl.handle.net/10722/294084 |
ISSN | 2023 Impact Factor: 1.5 2023 SCImago Journal Rankings: 2.022 |
ISI Accession Number ID |
DC Field | Value | Language |
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dc.contributor.author | Lu, JH | - |
dc.contributor.author | MOUQUIN, V | - |
dc.date.accessioned | 2020-11-23T08:26:06Z | - |
dc.date.available | 2020-11-23T08:26:06Z | - |
dc.date.issued | 2017 | - |
dc.identifier.citation | Advances in Mathematics, 2017, v. 306, p. 1209-1261 | - |
dc.identifier.issn | 0001-8708 | - |
dc.identifier.uri | http://hdl.handle.net/10722/294084 | - |
dc.description | Link to Open Archive | - |
dc.description.abstract | For 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.language | eng | - |
dc.publisher | Academic Press. The Journal's web site is located at http://www.elsevier.com/locate/aim | - |
dc.relation.ispartof | Advances in Mathematics | - |
dc.subject | Poisson geometry | - |
dc.subject | Flag varieties | - |
dc.subject | T-leaves | - |
dc.subject | Generalized Bruhat cells | - |
dc.title | On The T-leaves Of Some Poisson Structures Related To Products Of Flag Varieties | - |
dc.type | Article | - |
dc.identifier.email | Lu, JH: jhluhku@hku.hk | - |
dc.identifier.authority | Lu, JH=rp00753 | - |
dc.description.nature | link_to_subscribed_fulltext | - |
dc.identifier.doi | 10.1016/j.aim.2016.11.008 | - |
dc.identifier.scopus | eid_2-s2.0-84995545949 | - |
dc.identifier.hkuros | 319318 | - |
dc.identifier.volume | 306 | - |
dc.identifier.spage | 1209 | - |
dc.identifier.epage | 1261 | - |
dc.identifier.isi | WOS:000409285100034 | - |
dc.publisher.place | United Kingdom | - |
dc.identifier.issnl | 0001-8708 | - |