The isomorphism problem for cominuscule Schubert varieties

• Edward Richmond ^[1] ; Mihail Tarigradschi ^[2] ; Weihong Xu ^[3]
  1. [1] Oklahoma State University

     Oklahoma State University

     Estados Unidos

     
  2. [2] Rutgers University

     Rutgers University

     City of New Brunswick, Estados Unidos

     
  3. [3] Department of Mathematics, Virginia Tech, Blacksburg, VA, USA

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• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 30, Nº. 3, 2024, págs. 1-17
• Idioma: inglés
• DOI: 10.1007/s00029-024-00927-5
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• Resumen

  • Cominuscule flag varieties generalize Grassmannians to other Lie types. Schubert varieties in cominuscule flag varieties are indexed by posets of roots labeled long/short.

    These labeled posets generalize Young diagrams. We prove that Schubert varieties in potentially different cominuscule flag varieties are isomorphic as varieties if and only if their corresponding labeled posets are isomorphic, generalizing the classification of Grassmannian Schubert varieties using Young diagrams by the last two authors. Our proof is type-independent.

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