Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911

   
 
 

 

A Giambelli formula for classical $ G/P$ spaces


Author: Harry Tamvakis
Journal: J. Algebraic Geom. 23 (2014), 245-278
DOI: https://doi.org/10.1090/S1056-3911-2013-00604-9
Published electronically: July 11, 2013
MathSciNet review: 3166391
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Abstract | References | Additional Information

Abstract: Let $ G$ be a classical complex Lie group, $ P$ any parabolic subgroup of $ G$, and $ G/P$ the corresponding partial flag variety. We prove an explicit combinatorial Giambelli formula which expresses an arbitrary Schubert class in $ \mathrm {H}^*(G/P)$ as a polynomial in certain special Schubert class generators. Our formula extends to one that applies to the torus-equivariant cohomology ring of $ G/P$ and to the setting of symplectic and orthogonal degeneracy loci.


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Additional Information

Harry Tamvakis
Affiliation: Department of Mathematics, University of Maryland, 1301 Mathematics Building, College Park, Maryland 20742
Email: harryt@math.umd.edu

DOI: https://doi.org/10.1090/S1056-3911-2013-00604-9
Received by editor(s): February 2, 2011
Received by editor(s) in revised form: May 18, 2011
Published electronically: July 11, 2013
Additional Notes: The author was supported in part by NSF Grant DMS-0901341.
Article copyright: © Copyright 2013 University Press, Inc.
The copyright for this article reverts to public domain 28 years after publication.

American Mathematical Society