Pattern avoidance and smoothness of closures for orbits of a symmetric subgroup in the flag variety

2009/04/29 by William M. McGovern, McGovern, William M., Peter E. Trapa +1
Mathematics · #22E10 #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Algebraic Geometry and Number Theory #Combinatorics (math.CO) #FOS: Mathematics #Finite Group Theory Research #Representation Theory (math.RT) #math.CO #math.RT #msc:22E10

paper · pdf · doi:10.48550/arxiv.0904.4493

20 pages, 3 figures. Minor revisions (corrected typos and incorporated updates from arXiv:0905.0127v2)

openalex publication_date 2009/04/29 · arxiv created 2012/03/19 · arxiv updated 2012/03/20 · openalex created_date 2025/10/27 · openalex updated_date 2026/07/28

Abstract

We give a pattern avoidance criterion to classify the orbits of Sp(p,C) x Sp(q,C) (resp. GL(n,C)) on the flag variety of type C_p+q (resp. D_n) with rationally smooth closure. We show that all such orbit closures fiber (with smooth fiber) over a smaller flag variety, and hence are in fact smooth. In addition we prove that the classification is insensitive to isogeny.

Citations

• Closures of K-orbits in the flag variety for U(p,q)

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• Closures of K-orbits in the flag variety for GL(2n)
• Closures of O_n orbits in the flag variety for GL_n, II
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• Regular orbits of symmetric subgroups on partial flag varieties