Classification of Levi-spherical Schubert varieties
Yibo Gao, Reuven Hodges, Alexander Yong

TL;DR
This paper provides a combinatorial classification of Levi-spherical Schubert varieties in the complete flag manifold, confirming a conjecture and introducing a new Coxeter element formulation using key polynomial theory.
Contribution
It establishes a complete combinatorial classification of Levi-spherical Schubert varieties, confirming a prior conjecture and linking it to Coxeter elements and Demazure module characters.
Findings
Classification confirms the conjecture about Levi-spherical Schubert varieties.
New formulation in terms of standard Coxeter elements.
Uses key polynomial theory to prove the classification.
Abstract
A Schubert variety in the complete flag manifold is Levi-spherical if the action of a Borel subgroup in a Levi subgroup of a standard parabolic has a dense orbit. We give a combinatorial classification of these Schubert varieties. This establishes a conjecture of the latter two authors, and a new formulation in terms of standard Coxeter elements. Our proof uses the theory of key polynomials (type A Demazure module characters).
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Taxonomy
TopicsAdvanced Combinatorial Mathematics · Advanced Algebra and Geometry · Advanced Mathematical Identities
