One-skeleton posets of Bruhat interval polytopes
Christian Gaetz

TL;DR
This paper studies the 1-skeleton posets of Bruhat interval polytopes, proving they form lattices, classifying when these polytopes are simple, and determining conditions for smooth torus orbit closures in Schubert varieties.
Contribution
It establishes that the 1-skeleton posets are lattices and classifies the simplicity of Bruhat interval polytopes, resolving several open problems and conjectures.
Findings
1-skeleton posets of Bruhat interval polytopes are lattices
Classified when these polytopes are simple
Identified conditions for smooth torus orbit closures in Schubert varieties
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.
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · Advanced Algebra and Geometry · Geometric and Algebraic Topology
