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Article: DOUBLE BRUHAT CELLS AND SYMPLECTIC GROUPOIDS
Title | DOUBLE BRUHAT CELLS AND SYMPLECTIC GROUPOIDS |
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Authors | |
Issue Date | 2017 |
Publisher | Birkhaeuser Science. The Journal's web site is located at http://www.springer.com/mathematics/algebra/journal/31 |
Citation | Transformation Groups, 2017, v. 23, p. 765-800 How to Cite? |
Abstract | Let G be a connected complex semisimple Lie group, equipped with a standard multiplicative Poisson structure π st determined by a pair of opposite Borel subgroups (B, B_). We prove that for each υ in the Weyl group W of G, the double Bruhat cell G υ,υ = BυB Ω B_υB_ in G, together with the Poisson structure π st, is naturally a Poisson groupoid over the Bruhat cell BυB/B in the flag variety G/B. Correspondingly, every symplectic leaf of π st in G υ,υ is a symplectic groupoid over BυB/B. For u, υ ϵ W, we show that the double Bruhat cell (G u,υ , π st) has a naturally defined left Poisson action by the Poisson groupoid (G u,υ , π st) and a right Poisson action by the Poisson groupoid (G u,υ , π st), and the two actions commute. Restricting to symplectic leaves of π st, one obtains commuting left and right Poisson actions on symplectic leaves in G u,υ by symplectic leaves in G u,u and G υ,υ as symplectic groupoids. |
Persistent Identifier | http://hdl.handle.net/10722/293377 |
ISSN | 2023 Impact Factor: 0.4 2023 SCImago Journal Rankings: 0.844 |
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 | 2020-11-23T08:15:51Z | - |
dc.date.available | 2020-11-23T08:15:51Z | - |
dc.date.issued | 2017 | - |
dc.identifier.citation | Transformation Groups, 2017, v. 23, p. 765-800 | - |
dc.identifier.issn | 1083-4362 | - |
dc.identifier.uri | http://hdl.handle.net/10722/293377 | - |
dc.description.abstract | Let G be a connected complex semisimple Lie group, equipped with a standard multiplicative Poisson structure π st determined by a pair of opposite Borel subgroups (B, B_). We prove that for each υ in the Weyl group W of G, the double Bruhat cell G υ,υ = BυB Ω B_υB_ in G, together with the Poisson structure π st, is naturally a Poisson groupoid over the Bruhat cell BυB/B in the flag variety G/B. Correspondingly, every symplectic leaf of π st in G υ,υ is a symplectic groupoid over BυB/B. For u, υ ϵ W, we show that the double Bruhat cell (G u,υ , π st) has a naturally defined left Poisson action by the Poisson groupoid (G u,υ , π st) and a right Poisson action by the Poisson groupoid (G u,υ , π st), and the two actions commute. Restricting to symplectic leaves of π st, one obtains commuting left and right Poisson actions on symplectic leaves in G u,υ by symplectic leaves in G u,u and G υ,υ as symplectic groupoids. | - |
dc.language | eng | - |
dc.publisher | Birkhaeuser Science. The Journal's web site is located at http://www.springer.com/mathematics/algebra/journal/31 | - |
dc.relation.ispartof | Transformation Groups | - |
dc.rights | Accepted Manuscript (AAM) This 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.title | DOUBLE BRUHAT CELLS AND SYMPLECTIC GROUPOIDS | - |
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.description.nature | link_to_subscribed_fulltext | - |
dc.identifier.doi | 10.1007/s00031-017-9437-6 | - |
dc.identifier.scopus | eid_2-s2.0-85027008293 | - |
dc.identifier.hkuros | 319317 | - |
dc.identifier.volume | 23 | - |
dc.identifier.spage | 765 | - |
dc.identifier.epage | 800 | - |
dc.identifier.isi | WOS:000440820400008 | - |
dc.publisher.place | Switzerland | - |