The Orbits of the Symplectic Group on the Flag Manifold

2014/11/10 by Anna Bertiger, Bertiger, Anna
Mathematics · #05E40 #06A11 #14Q99 #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG #msc:05E40 #msc:06A11 #msc:14Q99

paper · pdf · doi:10.48550/arxiv.1411.2302

12 pages, 13 figures

arxiv created 2014/11/10 · arxiv updated 2014/11/11

Abstract

We examine the orbits of the (complex) symplectic group, Sp_n, on the flag manifold, \mathscrFℓ(ℂ²ⁿ), in a very concrete way. We use two approaches: we Gröbner degenerate the orbits to unions of Schubert varieties (for a equations of a particular union of Schubert varieties see \citeNWunions) and we find a subset A of the orbit closures containing the basic elements of the poset of orbit closures under containment, which represent the geometric and combinatorial building blocks for the orbit closures.

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