Governing singularities of symmetric orbit closures

Woo, Alexander; Wyser, Benjamin; Yong, Alexander

doi:10.2140/ant.2018.12.173

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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

DOI: 10.2140/ant.2018.12.173

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 ${GL}_{p} \times {GL}_{q}$ 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

Milestones

Received: 10 June 2017

Accepted: 17 August 2017

Published: 13 March 2018

Authors

Alexander Woo
Department of Mathematics University of Idaho Moscow, ID United States

Benjamin J. Wyser
Department of Mathematics University of Illinois at Urbana-Champaign Urbana, IL United States	Department of Mathematics Oklahoma State University Stillwater, OK United States

Alexander Yong
Department of Mathematics University of Illinois at Urbana-Champaign Urbana, IL United States

Vol. 12, No. 1, 2018