Séminaire Lotharingien de Combinatoire, 89B.1 (2023), 12 pp.
Christian Gaetz
Bruhat Interval Polytopes, 1-Skeleton Lattices, and Smooth Torus Orbit Closures
Abstract.
Introduced by Kodama and Williams, Bruhat interval polytopes are generalized permutohedra closely connected to the study of torus orbit closures and total positivity in Schubert varieties. We show that the 1-skeleton posets of these polytopes are lattices and classify when the polytopes are simple, thereby resolving open problems and conjectures of Fraser, of Lee-Masuda, and of Lee-Masuda-Park. In particular, we classify when generic torus orbit closures in Schubert varieties are smooth.
Received: November 15, 2022.
Accepted: February 20, 2023.
Final version: April 1, 2023.
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