Restricting Schubert classes

Details Restricting Schubert classes Restricting Schubert classes

1999-07-14

arxiv.org/abs/math/9907092v2

Mathematics

Algebraic Geometry

9 pages; AMS-TEX, misprints corrected, exposition improved

Scientific paper

Let V be a 2n-dimensional complex symplectic space. Let G' be the Lagrangian Grassmannian of maximal isotropic subspaces of V embedded via the inclusion i into the Grassmannian G of all n-dimensional subspaces of V. We discuss the restriction via i* of a Schubert class from H(G), as an integral linear combination of Schubert classes in H(G'). Among the main tools we mention Stembridge's results on shifted tableaux. Using these results and a generalization of the Macdonald-You identity from an earlier author's paper, we establish several related algebro-geometric formulas.

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