2:00 pm, Lecture Hall 4
Equivariant Pieri rules for Isotropic Grassmannians
Vijay Ravikumar
TIFR, Mumbai.
26-03-14

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Abstract

Let X be an isotropic Grassmannian of type B or C. In this talk we give a torus equivariant Pieri rule for X: that is, we describe the structure constants expressing the product of an arbitrary Schubert class and a special Schubert class with respect to the Schubert basis for the torus equivariant cohomology ring of X. We do this by expressing each structure constant as a sum of restrictions of Schubert classes to torus fixed points in the equivariant cohomology ring of an ordinary (type A) Grassmannian. These restrictions are well studied, for example they are equal to Kostant-Kumar polynomials, and have a determinantal formula given by Lakshmibai, Raghavan, and Sankaran.