Excited Young diagrams and equivariant Schubert calculus

Ikeda, Takeshi; Naruse, Hiroshi

doi:10.1090/S0002-9947-09-04879-X

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

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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