Pieri-type formulas for maximal isotropic Grassmannians via triple intersections

Abstract

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 explicit description of the intersection of two Schubert varieties, from which the multiplicities (which are powers of 2) in the Pieri-type formula are deduced.

LaTeX 2e, 24 pages (9 pages is an appendix detailing the proof in the symplectic case). Expanded version of MSRI preprint 1997-062