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Article: Bott–samelson Atlases, Total Positivity, And Poisson Structures On Some Homogeneous Spaces

TitleBott–samelson Atlases, Total Positivity, And Poisson Structures On Some Homogeneous Spaces
Authors
Issue Date2020
PublisherBirkhaeuser Verlag AG. The Journal's web site is located at http://link.springer.de/link/service/journals/00029/index.htm
Citation
Selecta Mathematica, 2020, v. 26, p. article no. 70 How to Cite?
AbstractLet G be a connected and simply connected complex semisimple Lie group. For a collection of homogeneous G-spaces G/Q, we construct a finite atlas ABS(G/Q) on G/Q, called the Bott–Samelson atlas, and we prove that all of its coordinate functions are positive with respect to the Lusztig positive structure on G/Q. We also show that the standard Poisson structure πG/Q on G/Q is presented, in each of the coordinate charts of ABS(G/Q), as a symmetric Poisson CGL extension (or a certain localization thereof) in the sense of Goodearl–Yakimov, making (G/Q,πG/Q,ABS(G/Q)) into a Poisson–Ore variety. In addition, all coordinate functions in the Bott–Samelson atlas are shown to have complete Hamiltonian flows with respect to the Poisson structure πG/Q. Examples of G/Q include G itself, G/T, G/B, and G/N, where T⊂G is a maximal torus, B⊂G a Borel subgroup, and N the uniradical of B.
Persistent Identifierhttp://hdl.handle.net/10722/293376
ISSN
2023 Impact Factor: 1.2
2023 SCImago Journal Rankings: 1.715
ISI Accession Number ID

 

DC FieldValueLanguage
dc.contributor.authorLu, JH-
dc.contributor.authorYU, S-
dc.date.accessioned2020-11-23T08:15:51Z-
dc.date.available2020-11-23T08:15:51Z-
dc.date.issued2020-
dc.identifier.citationSelecta Mathematica, 2020, v. 26, p. article no. 70-
dc.identifier.issn1022-1824-
dc.identifier.urihttp://hdl.handle.net/10722/293376-
dc.description.abstractLet G be a connected and simply connected complex semisimple Lie group. For a collection of homogeneous G-spaces G/Q, we construct a finite atlas ABS(G/Q) on G/Q, called the Bott–Samelson atlas, and we prove that all of its coordinate functions are positive with respect to the Lusztig positive structure on G/Q. We also show that the standard Poisson structure πG/Q on G/Q is presented, in each of the coordinate charts of ABS(G/Q), as a symmetric Poisson CGL extension (or a certain localization thereof) in the sense of Goodearl–Yakimov, making (G/Q,πG/Q,ABS(G/Q)) into a Poisson–Ore variety. In addition, all coordinate functions in the Bott–Samelson atlas are shown to have complete Hamiltonian flows with respect to the Poisson structure πG/Q. Examples of G/Q include G itself, G/T, G/B, and G/N, where T⊂G is a maximal torus, B⊂G a Borel subgroup, and N the uniradical of B.-
dc.languageeng-
dc.publisherBirkhaeuser Verlag AG. The Journal's web site is located at http://link.springer.de/link/service/journals/00029/index.htm-
dc.relation.ispartofSelecta Mathematica-
dc.rightsThis is a post-peer-review, pre-copyedit version of an article published in [insert journal title]. The final authenticated version is available online at: https://doi.org/[insert DOI]-
dc.titleBott–samelson Atlases, Total Positivity, And Poisson Structures On Some Homogeneous Spaces-
dc.typeArticle-
dc.identifier.emailLu, JH: jhluhku@hku.hk-
dc.identifier.authorityLu, JH=rp00753-
dc.description.naturelink_to_subscribed_fulltext-
dc.identifier.doi10.1007/s00029-020-00595-1-
dc.identifier.scopuseid_2-s2.0-85092395625-
dc.identifier.hkuros319314-
dc.identifier.volume26-
dc.identifier.spagearticle no. 70-
dc.identifier.epagearticle no. 70-
dc.identifier.isiWOS:000578384100001-
dc.publisher.placeSwitzerland-

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