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.Comment: 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 change

Lakshmibai, V.

Raghavan, K. N.

Sankaran, P.

English

arXiv

Let V be an n-dimensional complex vector space and Gd,n the Grassmannian of d-dimensional linear subspaces of V. The authors consider the T-equivariant integral cohomology ring H of Gd,n. It is known that the equivariant Schubert classes form a basis for H over the T-equivariant cohomology ring of a point. The main result of the article is a determinantal formula for the restriction to a torus fixed point of the equivariant class of a Schubert subvariety in H. To prove this result, the authors use Gröbner degeneration technique. As a corollary, an equivariant version of Giambelli formula is obtained

Equivariant Giambelli and determinantal restriction formulas for the Grassmannian

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