A Giambelli formula for isotropic Grassmannians

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 it...

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Bibliographic Details
Published in:Selecta mathematica (Basel, Switzerland) Switzerland), 2017-04, Vol.23 (2), p.869-914
Main Authors: Buch, Anders Skovsted, Kresch, Andrew, Tamvakis, Harry
Format: Article
Language:English
Subjects:
Mathematics
Mathematics and Statistics
Polynomials
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Summary: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.
ISSN:1022-1824
1420-9020
DOI:10.1007/s00029-016-0250-1