Pieri-type formulas for maximal isotropic Grassmannians via triple intersections

Volume 82 / 1999

Frank Sottile 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.

Authors

  • Frank Sottile

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