Schubert Classes in the Equivariant K-Theory and Equivariant Cohomology of the Grassmannian

Abstract

We give positive formulas for the restriction of a Schubert Class to a T-fixed point in the equivariant K-theory and equivariant cohomology of the Grassmannian. Our formulas rely on a result of Kodiyalam-Raghavan and Kreiman-Lakshmibai, which gives an equivariant Grobner degeneration of a Schubert variety in the neighborhood of a T-fixed point of the Grassmannian.

27 pages. Version 2 contains more discussion of nonintersecting path families and additional references

References in corpus (3)

• On multiplicities of points on Schubert varieties in Grassmannians
• Schubert Classes in the Equivariant K-Theory and Equivariant Cohomology of the Lagrangian Grassmannian
• Local Properties of Richardson Varieties in the Grassmannian via a Bounded Robinson-Schensted-Knuth Correspondence

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• Skew hook formula for $d$-complete posets
• Schubert Classes in the Equivariant K-Theory and Equivariant Cohomology of the Lagrangian Grassmannian
• Equivariant Littlewood-Richardson Skew Tableaux
• Reverse plane partitions of skew staircase shapes and $q$-Euler numbers
• Some degenerations of Kazhdan-Lusztig ideals and multiplicities of Schubert varieties
• On the tensor product of two basic representations of $U_v({\widehat{sl}}_e)$
• Hook-content formula using excited Young diagrams
• Excited Young diagrams, equivariant K-theory, and Schubert varieties