TY - JOUR

T1 - Excited Young diagrams and equivariant Schubert calculus

AU - Ikeda, Takeshi

AU - Naruse, Hiroshi

N1 - Copyright:
Copyright 2010 Elsevier B.V., All rights reserved.

PY - 2009/10

Y1 - 2009/10

N2 - 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.

AB - 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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U2 - 10.1090/S0002-9947-09-04879-X

DO - 10.1090/S0002-9947-09-04879-X

M3 - Article

AN - SCOPUS:77950631522

SN - 0002-9947

VL - 361

SP - 5193

EP - 5221

JO - Transactions of the American Mathematical Society

JF - Transactions of the American Mathematical Society

IS - 10

ER -