Poisson structures on complex flag manifolds associated with real forms

2003/09/19 by Philip Foth, Jiang-Hua Lu, Foth, Philip +1
Mathematics · #53D17 #Advanced Algebra and Geometry #Advanced Topics in Algebra #FOS: Mathematics #Geometry and complex manifolds #Representation Theory (math.RT) #Symplectic Geometry (math.SG) #math.RT #math.SG #msc:53D17

paper · pdf · doi:10.48550/arxiv.math/0309334

11 pages

arxiv created 2003/09/19 · openalex publication_date 2003/09/19 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For a complex semi-simple group G and its real form G0 we define a Poisson structure on the flag variety of G such that all the Bruhat cells (for a suitable choice of a Borel subgroup of G) as well as all the G0-orbits are Poisson submanifolds. We show that each intersection of a G0-orbit with a Bruhat cell is a regular Poisson submanifold and we compute the dimensions of its symplectic leaves.

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