Classification of Levi-spherical Schubert varieties

• Yibo Gao ^[1] ; Reuven Hodges ^[2] ; Alexander Yong ^[3]
  1. [1] Peking University

     Peking University

     China

     
  2. [2] University of Kansas

     University of Kansas

     City of Lawrence, Estados Unidos

     
  3. [3] University of Illinois at Urbana-Champaign, USA

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• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 29, Nº. 4, 2023
• Idioma: inglés
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• Resumen

  • 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 an open 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 and contributes to the theory of key polynomials (type A Demazure module characters).