Excited Young diagrams and equivariant Schubert calculus
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- by Takeshi Ikeda and Hiroshi Naruse PDF
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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 âexcited Young diagramsâ, 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.References
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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
- ORCID: 0000-0002-0122-5450
- Email: rdcv1654@cc.okayama-u.ac.jp
- Received by editor(s): September 4, 2007
- Published electronically: April 30, 2009
- © Copyright 2009
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Trans. Amer. Math. Soc. 361 (2009), 5193-5221
- MSC (2000): Primary 05E15; Secondary 14N15, 14M15, 05E05
- DOI: https://doi.org/10.1090/S0002-9947-09-04879-X
- MathSciNet review: 2515809