2006/04/13 by Ion Alexandru Mihai, Mihai, Ion Alexandru
Mathematics · #14L35 #14M15 #14M17 #17B10 #17B45 #20G05 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #math.AG #msc:14L35 #msc:14M15 #msc:14M17 #msc:17B10 #msc:17B45 #msc:20G05
paper · pdf · doi:10.48550/arxiv.math/0604323
32 pages
arxiv created 2006/04/13 · openalex publication_date 2006/04/13 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We define the odd symplectic grassmannians and flag manifolds, which are smooth projective varieties equipped with an action of the odd symplectic group and generalizing the usual symplectic grassmannians and flag manifolds. Contrary to the latter, which are the flag manifolds of the symplectic group, the varieties we introduce are not homogeneous. We argue nevertheless that in many respects the odd symplectic grassmannians and flag manifolds behave like homogeneous varieties; in support of this claim, we compute the automorphism group of the odd symplectic grassmannians, and we prove a Borel-Weil type theorem for the odd symplectic group.