Pieri-type formulas for maximal isotropic Grassmannians via triple intersections

Frank Sottile

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 (powers of 2) in the Pieri-type formula are deduced.



The manuscript in postscript.
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