On multiplicities of points on Schubert varieties in Grassmannians

Abstract

We answer some questions related to multiplicity formulas by Rosenthal and Zelevinsky and by Lakshmibai and Weyman for points on Schubert varieties in Grassmannians. In particular, we give combinatorial interpretations in terms of nonintersecting lattice paths of these formulas, which makes the equality of the two formulas immediately obvious. Furthermore we provide an alternative determinantal formula for these multiplicities, and we show that they count semistandard tableaux of unusual shapes.

10 pages, AmS-TeX

Cited by in corpus (6)

• Governing Singularities of Schubert Varieties
• Schubert Classes in the Equivariant K-Theory and Equivariant Cohomology of the Grassmannian
• Schubert Classes in the Equivariant K-Theory and Equivariant Cohomology of the Lagrangian Grassmannian
• Multiplicities of the Most Singular Point on Schubert varieties on Gl(n)/B for n=5,6
• Initial ideals of tangent cones to Richardson varieties in the Orthogonal Grassmannian via a Orthogonal-Bounded-RSK-Correspondence
• Some degenerations of Kazhdan-Lusztig ideals and multiplicities of Schubert varieties