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Excited Young diagrams and equivariant Schubert calculus. (English) Zbl 1229.05287
Summary: 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.

MSC:
05E15 Combinatorial aspects of groups and algebras (MSC2010)
14N15 Classical problems, Schubert calculus
14M15 Grassmannians, Schubert varieties, flag manifolds
05E05 Symmetric functions and generalizations
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