Pieri-type formulas for maximal isotropic Grassmannians via triple intersections
Volume 82 / 1999
Colloquium Mathematicum 82 (1999), 49-63
DOI: 10.4064/cm-82-1-49-63
Abstract
We give an elementary proof of the Pieri-type formula in the cohomology ring of a Grassmannian of maximal isotropic subspaces of an orthogonal or symplectic vector space. This proof proceeds by explicitly computing a triple intersection of Schubert varieties. The multiplicities (which are powers of 2) in the Pieri-type formula are seen to arise from the intersection of a collection of quadrics with a linear space.
