A Giambelli formula for isotropic Grassmannians

• Anders Skovsted Buch ^[1] ; Andrew Kresch ^[2] ; Harry Tamvakis ^[3]
  1. [1] Rutgers University

     Rutgers University

     City of New Brunswick, Estados Unidos

     
  2. [2] University of Zurich

     University of Zurich

     Zürich, Suiza

     
  3. [3] University of Maryland

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• Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 23, Nº. 2, 2017, págs. 869-914
• Idioma: inglés
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• Resumen

  • Let X be a symplectic or odd orthogonal Grassmannian. We prove a Giambelli formula which expresses an arbitrary Schubert class in H∗(X,Z) as a polynomial in certain special Schubert classes. This polynomial, which we call a theta polynomial, is defined using raising operators, and we study its image in the ring of Billey–Haiman Schubert polynomials.