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

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 GLp × GLq acting on the classical flag variety. We prove that all reasonable singularity properties can be classified in terms of interval patterns of clans.

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flag variety, Schubert variety, symmetric subgroup, interval pattern avoidance
Mathematical Subject Classification 2010
Primary: 14M17
Secondary: 05E40, 14M15, 14M27
Received: 10 June 2017
Accepted: 17 August 2017
Published: 13 March 2018
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