Pieri-type formulas for maximal isotropic Grassmannains via triple intersections

Details Pieri-type formulas for maximal isotropic Grassmannains via triple intersections Pieri-type formulas for maximal isotropic Grassmannains via triple intersections

1997-06-09

arxiv.org/abs/math/9706217v1

Mathematics

Algebraic Geometry

Scientific paper

We give an elementary proof of the Pieri-type formula in the cohomology of a Grassmannian of maximal isotropic subspaces of an odd orthogonal or symplectic vector space. This proof proceeds by explicitly computing a triple intersection of Schubert varieties. The decisive step is an exact description of the intersection of two Schubert varieties, from which the multiplicities (which are powers of 2) in the Pieri-type formula are immediately obvious.

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