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A Giambelli formula for isotropic Grassmannians


Buch, Anders Skovsted; Kresch, Andrew; Tamvakis, Harry (2017). A Giambelli formula for isotropic Grassmannians. Selecta Mathematica, 23(2):869-914.

Abstract

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.

Abstract

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.

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Additional indexing

Item Type:Journal Article, not refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Language:English
Date:April 2017
Deposited On:22 May 2017 16:29
Last Modified:09 Dec 2017 01:02
Publisher:Birkhäuser
ISSN:1022-1824
Publisher DOI:https://doi.org/10.1007/s00029-016-0250-1

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