Equivariant Giambelli and determinantal restriction formulas for the Grassmannian

2005/06/01 by V. Lakshmibai, Lakshmibai, V., K. N. Raghavan +4
Mathematics · #14M15 #Advanced Algebra and Geometry #Advanced Combinatorial Mathematics #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG #msc:14M15

paper · pdf · doi:10.48550/arxiv.math/0506015

16 pages, 3 figures, LaTex, uses epsfig and psfrag; for the revised version: title changed; Proof of Theorem 3 changed; 3 references added and 1 deleted; other minor changes

openalex publication_date 2005/06/01 · arxiv created 2005/09/15 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The main result of the paper is a determinantal formula for the restriction to a torus fixed point of the equivariant class of a Schubert subvariety in the torus equivariant integral cohomology ring of the Grassmannian. As a corollary, we obtain an equivariant version of the Giambelli formula.

Related

• Schubert Classes in the Equivariant K-Theory and Equivariant Cohomology of the Grassmannian
• Giambelli formulae for the equivariant quantum cohomology of the Grassmannian
• Schubert classes in the equivariant cohomology of the Lagrangian Grassmannian
• Schubert Classes in the Equivariant K-Theory and Equivariant Cohomology of the Lagrangian Grassmannian
• Equivariant Schubert Calculus