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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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Excited Young diagrams and equivariant Schubert calculus
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by Takeshi Ikeda and Hiroshi Naruse PDF
Trans. Amer. Math. Soc. 361 (2009), 5193-5221 Request permission


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:
  • Hiroshi Naruse
  • Affiliation: Graduate School of Education, Okayama University, Okayama 700-8530, Japan
  • ORCID: 0000-0002-0122-5450
  • Email:
  • 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:
  • MathSciNet review: 2515809