The Orbits of the Symplectic Group on the Flag Manifold

Abstract

We examine the orbits of the (complex) symplectic group, $S{p}_n$, on the flag manifold, $\mathcal{F}\ell ({\mathbb{C}}^{2n})$, 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 \cite{NWunions}) and we find a subset $\mathcal{A}$ 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.

12 pages, 13 figures

Cited by in corpus (2)

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