Symmetric subgroup actions on isotropic Grassmannians

JOURNAL OF ALGEBRA

卷:337

Article

Huang, Huajun¹  He, Hongyu² 

[1] Auburn Univ, Dept Math & Stat, Auburn, AL 36849 USA

[2] Louisiana State Univ, Dept Math, Baton Rouge, LA 70803 USA

关键词: Grassmannian;    Symmetric subgroup;    Sesquilinear form;    Invariant;    Stabilizer;    Bruhat order;    Inclusion order;   

DOI  :  10.1016/j.jalgebra.2011.04.022

来源: Elsevier

【 摘 要 】

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 G(1) X G(2). We explicitly parameterize the H-orbits in Gr(G)(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 boolean AND G(0) and H(0) orbits are also explicitly described. (C) 2011 Elsevier Inc. All rights reserved.

【 授权许可】

Free