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A Pieri-type formula for even orthogonal Grassmannians

Tom 178 / 2003

Piotr Pragacz, Jan Ratajski Fundamenta Mathematicae 178 (2003), 49-96 MSC: 14M15, 05E05. DOI: 10.4064/fm178-1-2

Streszczenie

We study the cohomology ring of the Grassmannian $G$ of isotropic $n$-subspaces of a complex $2m$-dimensional vector space, endowed with a nondegenerate orthogonal form (here $1\le n < m$). We state and prove a formula giving the Schubert class decomposition of the cohomology products in $H^*(G)$ of general Schubert classes by “special Schubert classes”, i.e. the Chern classes of the dual of the tautological vector bundle of rank $n$ on $G$. We discuss some related properties of reduced decompositions of “barred permutations” with even numbers of bars, and divided differences associated with the even orthogonal group $SO(2m)$.

Autorzy

  • Piotr PragaczInstitute of Mathematics
    Polish Academy of Sciences
    /Sniadeckich 8
    P.O. Box 21
    00-956 Warszawa 10, Poland
    e-mail
  • Jan RatajskiING Nationale-Nederlanden Polska S.A.
    Ludna 2
    00-406 Warszawa, Poland
    e-mail

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