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ArticleOriginal scientific text

Title

Pieri-type formulas for maximal isotropic Grassmannians via triple intersections

Authors 1

Affiliations

  1. Department of Mathematics, University of Wisconsin, Van Vleck Hall, 480 Lincoln Drive, Madison, WI 53706-1388, U.S.A.

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.

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Colloquium Mathematicum
1999/82/1
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Pages:
49-63
Main language of publication
English
Received
1999-03-19
Published
1999
Exact and natural sciences