2009/02/12 by Milen Yakimov, Yakimov, Milen · 1 citation
Mathematics · #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #Combinatorics (math.CO) #FOS: Mathematics #Symplectic Geometry (math.SG) #math.CO #math.SG
paper · pdf · doi:10.48550/arxiv.0902.2181
5 pages, AMS Latex
arxiv created 2009/02/12 · openalex publication_date 2009/02/12 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We prove that the standard Poisson structure on the Grassmannian Gr(k, n) is invariant under the action of the Coxeter element c =(1 2 ... n). In particular, its symplectic foliation is invariant under c. As a corollary, we obtain a second, Poisson geometric proof of the result of Knutson, Lam, and Speyer that the Coxeter element c interchanges the Lusztig strata of Gr(k, n). We also relate the main result to known anti-invariance properties of the standard Poisson structures on cominuscule flag varieties.