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- Publisher Website: 10.1016/j.indag.2014.07.011
- Scopus: eid_2-s2.0-84908043562
- WOS: WOS:000343788400012
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Article: On the T-leaves and the ranks of a Poisson structure on twisted conjugacy classes
Title | On the T-leaves and the ranks of a Poisson structure on twisted conjugacy classes |
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Authors | |
Keywords | Poisson structures Spherical conjugcy classes |
Issue Date | 2014 |
Citation | Indagationes Mathematicae, 2014 How to Cite? |
Abstract | Let 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 Identifier | http://hdl.handle.net/10722/202992 |
ISI Accession Number ID |
DC Field | Value | Language |
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dc.contributor.author | Lu, J | en_US |
dc.date.accessioned | 2014-09-19T11:06:56Z | - |
dc.date.available | 2014-09-19T11:06:56Z | - |
dc.date.issued | 2014 | en_US |
dc.identifier.citation | Indagationes Mathematicae, 2014 | en_US |
dc.identifier.uri | http://hdl.handle.net/10722/202992 | - |
dc.description.abstract | Let 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.language | eng | en_US |
dc.relation.ispartof | Indagationes Mathematicae | en_US |
dc.subject | Poisson structures | - |
dc.subject | Spherical conjugcy classes | - |
dc.title | On the T-leaves and the ranks of a Poisson structure on twisted conjugacy classes | en_US |
dc.type | Article | en_US |
dc.identifier.email | Lu, J: jhluhku@hku.hk | en_US |
dc.identifier.authority | Lu, J=rp00753 | en_US |
dc.identifier.doi | 10.1016/j.indag.2014.07.011 | en_US |
dc.identifier.scopus | eid_2-s2.0-84908043562 | - |
dc.identifier.hkuros | 239773 | en_US |
dc.identifier.isi | WOS:000343788400012 | - |