Vol. 12, No. 1, 2018

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Governing singularities of symmetric orbit closures

Alexander Woo, Benjamin J. Wyser and Alexander Yong

Vol. 12 (2018), No. 1, 173–225
Abstract

We develop interval pattern avoidance and Mars–Springer ideals to study singularities of symmetric orbit closures in a flag variety. This paper focuses on the case of the Levi subgroup ${GL}_{p}×{GL}_{q}$ acting on the classical flag variety. We prove that all reasonable singularity properties can be classified in terms of interval patterns of clans.

Keywords
flag variety, Schubert variety, symmetric subgroup, interval pattern avoidance
Mathematical Subject Classification 2010
Primary: 14M17
Secondary: 05E40, 14M15, 14M27