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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Excited Young diagrams and equivariant Schubert calculus


Authors: Takeshi Ikeda and Hiroshi Naruse
Journal: Trans. Amer. Math. Soc. 361 (2009), 5193-5221
MSC (2000): Primary 05E15; Secondary 14N15, 14M15, 05E05
Published electronically: April 30, 2009
MathSciNet review: 2515809
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Abstract: We describe the torus-equivariant cohomology ring of isotropic Grassmannians by using a localization map to the torus fixed points. We present two types of formulas for equivariant Schubert classes of these homogeneous spaces. The first formula involves combinatorial objects which we call ``excited Young diagrams'', and the second one is written in terms of factorial Schur $ Q$- or $ P$-functions. As an application, we give a Giambelli-type formula for the equivariant Schubert classes. We also give combinatorial and Pfaffian formulas for the multiplicity of a singular point in a Schubert variety.


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Additional Information

Takeshi Ikeda
Affiliation: Department of Applied Mathematics, Okayama University of Science, Okayama 700-0005, Japan
Email: ike@xmath.ous.ac.jp

Hiroshi Naruse
Affiliation: Graduate School of Education, Okayama University, Okayama 700-8530, Japan
Email: rdcv1654@cc.okayama-u.ac.jp

DOI: http://dx.doi.org/10.1090/S0002-9947-09-04879-X
PII: S 0002-9947(09)04879-X
Received by editor(s): September 4, 2007
Published electronically: April 30, 2009
Article copyright: © Copyright 2009 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.