# 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.

## Statistics

### Altmetrics

4 downloads since deposited on 22 May 2017
Detailed statistics

Item Type: Journal Article, refereed, original work 07 Faculty of Science > Institute of Mathematics 510 Mathematics English April 2017 22 May 2017 16:29 26 Jul 2017 00:00 Springer 1022-1824 https://doi.org/10.1007/s00029-016-0250-1

Preview
Content: Accepted Version
Filetype: PDF
Size: 446kB
View at publisher

## TrendTerms

TrendTerms displays relevant terms of the abstract of this publication and related documents on a map. The terms and their relations were extracted from ZORA using word statistics. Their timelines are taken from ZORA as well. The bubble size of a term is proportional to the number of documents where the term occurs. Red, orange, yellow and green colors are used for terms that occur in the current document; red indicates high interlinkedness of a term with other terms, orange, yellow and green decreasing interlinkedness. Blue is used for terms that have a relation with the terms in this document, but occur in other documents.
You can navigate and zoom the map. Mouse-hovering a term displays its timeline, clicking it yields the associated documents.