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Article: Poisson geometry of the Grothendieck resolution of a complex semisimple group

TitlePoisson geometry of the Grothendieck resolution of a complex semisimple group
Authors
KeywordsPoisson structure
Symplectic leaves
Grothendieck resolution
Steinberg fiber
Bruhat cell
Issue Date2007
PublisherIndependent University of Moscow.
Citation
Moscow Mathematical Journal, 2007, v. 7 n. 4, p. 613-642 How to Cite?
AbstractLet G be a complex semi-simple Lie group with a fixed pair of opposite Borel subgroups (B,B − ) . We study a Poisson structure π on G and a Poisson structure Π on the Grothendieck resolution X of G such that the Grothendieck map μ:(X,Π)→(G,π) is Poisson. We show that the orbits of symplectic leaves of π in G under the conjugation action by the Cartan subgroup H=B∩B – are intersections of conjugacy classes and Bruhat cells B ω B − , while the H -orbits of symplectic leaves of Π on X give desingularizations of intersections of Steinberg fibers and Bruhat cells in G . We also give birational Poisson isomorphisms from quotients by H×H of products of double Bruhat cells in G to intersections of Steinberg fibers and Bruhat cells.
Persistent Identifierhttp://hdl.handle.net/10722/75182
ISSN
2015 Impact Factor: 0.648
2015 SCImago Journal Rankings: 0.758

 

DC FieldValueLanguage
dc.contributor.authorEvens, Sen_HK
dc.contributor.authorLu, JHen_HK
dc.date.accessioned2010-09-06T07:08:43Z-
dc.date.available2010-09-06T07:08:43Z-
dc.date.issued2007en_HK
dc.identifier.citationMoscow Mathematical Journal, 2007, v. 7 n. 4, p. 613-642en_HK
dc.identifier.issn1609-3321en_HK
dc.identifier.urihttp://hdl.handle.net/10722/75182-
dc.description.abstractLet G be a complex semi-simple Lie group with a fixed pair of opposite Borel subgroups (B,B − ) . We study a Poisson structure π on G and a Poisson structure Π on the Grothendieck resolution X of G such that the Grothendieck map μ:(X,Π)→(G,π) is Poisson. We show that the orbits of symplectic leaves of π in G under the conjugation action by the Cartan subgroup H=B∩B – are intersections of conjugacy classes and Bruhat cells B ω B − , while the H -orbits of symplectic leaves of Π on X give desingularizations of intersections of Steinberg fibers and Bruhat cells in G . We also give birational Poisson isomorphisms from quotients by H×H of products of double Bruhat cells in G to intersections of Steinberg fibers and Bruhat cells.-
dc.languageengen_HK
dc.publisherIndependent University of Moscow.en_HK
dc.relation.ispartofMoscow Mathematical Journalen_HK
dc.subjectPoisson structure-
dc.subjectSymplectic leaves-
dc.subjectGrothendieck resolution-
dc.subjectSteinberg fiber-
dc.subjectBruhat cell-
dc.titlePoisson geometry of the Grothendieck resolution of a complex semisimple groupen_HK
dc.typeArticleen_HK
dc.identifier.emailLu, JH: jhlu@maths.hku.hken_HK
dc.identifier.authorityLu, J=rp00753en_HK
dc.description.naturelink_to_OA_fulltext-
dc.identifier.hkuros134964en_HK
dc.identifier.volume7-
dc.identifier.issue4-
dc.identifier.spage613-
dc.identifier.epage642-
dc.publisher.placeRussian Federation-

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