File Download

There are no files associated with this item.

  Links for fulltext
     (May Require Subscription)
Supplementary

Article: On the T-leaves and the ranks of a Poisson structure on twisted conjugacy classes

TitleOn the T-leaves and the ranks of a Poisson structure on twisted conjugacy classes
Authors
Issue Date2014
Citation
Indagationes Mathematicae, 2014 How to Cite?
AbstractLet G be a connected complex semisimple Lie group with a fixed maximal torus T and a Borel subgroup B⊃T. For an arbitrary automorphism θ of G, we introduce a holomorphic Poisson structure πθ on G which is invariant under the θ-twisted conjugation by T and has the property that every θ-twisted conjugacy class of G is a Poisson subvariety with respect to πθ. We describe the T-orbits of symplectic leaves, called T-leaves, of πθ and compute the dimensions of the symplectic leaves (i.e, the ranks) of πθ. We give the lowest rank of πθ in any given θ-twisted conjugacy class, and we relate the lowest possible rank locus of πθ in G with spherical θ-twisted conjugacy classes of G. In particular, we show that πθ vanishes somewhere on G if and only if θ induces an involution on the Dynkin diagram of G, and that in such a case a θ-twisted conjugacy class C contains a vanishing point of πθ if and only if C is spherical.
Persistent Identifierhttp://hdl.handle.net/10722/202992

 

DC FieldValueLanguage
dc.contributor.authorLu, Jen_US
dc.date.accessioned2014-09-19T11:06:56Z-
dc.date.available2014-09-19T11:06:56Z-
dc.date.issued2014en_US
dc.identifier.citationIndagationes Mathematicae, 2014en_US
dc.identifier.urihttp://hdl.handle.net/10722/202992-
dc.description.abstractLet G be a connected complex semisimple Lie group with a fixed maximal torus T and a Borel subgroup B⊃T. For an arbitrary automorphism θ of G, we introduce a holomorphic Poisson structure πθ on G which is invariant under the θ-twisted conjugation by T and has the property that every θ-twisted conjugacy class of G is a Poisson subvariety with respect to πθ. We describe the T-orbits of symplectic leaves, called T-leaves, of πθ and compute the dimensions of the symplectic leaves (i.e, the ranks) of πθ. We give the lowest rank of πθ in any given θ-twisted conjugacy class, and we relate the lowest possible rank locus of πθ in G with spherical θ-twisted conjugacy classes of G. In particular, we show that πθ vanishes somewhere on G if and only if θ induces an involution on the Dynkin diagram of G, and that in such a case a θ-twisted conjugacy class C contains a vanishing point of πθ if and only if C is spherical.en_US
dc.languageengen_US
dc.relation.ispartofIndagationes Mathematicaeen_US
dc.titleOn the T-leaves and the ranks of a Poisson structure on twisted conjugacy classesen_US
dc.typeArticleen_US
dc.identifier.emailLu, J: jhluhku@hku.hken_US
dc.identifier.authorityLu, J=rp00753en_US
dc.identifier.doi10.1016/j.indag.2014.07.011en_US
dc.identifier.hkuros239773en_US

Export via OAI-PMH Interface in XML Formats


OR


Export to Other Non-XML Formats