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arXiv · 2109.03724

Configuration Poisson groupoids of flags

Jiang-Hua Lu·Victor Mouquin·Shizhuo Yu
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Abstract

Let $G$ be a connected complex semi-simple Lie group and ${\mathcal{B}}$ its flag variety. For every positive integer $n$, we introduce a Poisson groupoid over ${\mathcal{B}}^n$, called the $n$th total configuration Poisson groupoid of flags of $G$, which contains a family of Poisson sub-groupoids whose total spaces are generalized double Bruhat cells and bases generalized Schubert cells. Certain symplectic leaves of these Poisson sub-groupoids are then shown to be symplectic groupoids over generalized Schubert cells. We also give explicit descriptions of symplectic leaves in three series of Poisson varieties associated to $G$.

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Jiang-Hua Lu, Victor Mouquin, Shizhuo Yu. 2021-09-08. Configuration Poisson groupoids of flags. https://arxiv.org/abs/2109.03724

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