Title

Symmetric subgroup actions on isotropic Grassmannians

Document Type

Article

Publication Date

7-1-2011

Abstract

Let G be the group preserving a nondegenerate sesquilinear form B on a vector space V, and H a symmetric subgroup of G of the type G1×G2. We explicitly parameterize the H-orbits in GrG(r), the Grassmannian of r-dimensional isotropic subspaces of V, by a complete set of H-invariants. We describe the Bruhat order in terms of the majorization relationship over a diagram of these H-invariants. The inclusion order, the stabilizer, the orbit dimension, the open H-orbits, the decompositions of an H orbit into H∩G0 and H0 orbits are also explicitly described. © 2011 Elsevier Inc.

Publication Source (Journal or Book title)

Journal of Algebra

First Page

141

Last Page

168

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