Geodesic
A Pieri-type formula for even orthogonal Grassmannians
Piotr Pragacz 1   ; Jan Ratajski 2
1 Institute of Mathematics Polish Academy of Sciences /Sniadeckich 8 P.O. Box 21 00-956 Warszawa 10, Poland
2 ING Nationale-Nederlanden Polska S.A. Ludna 2 00-406 Warszawa, Poland
Fundamenta Mathematicae, Tome 178 (2003) no. 1, pp. 49-96 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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 $SO(2m)$.
DOI : 10.4064/fm178-1-2
Keywords: study cohomology ring grassmannian isotropic n subspaces complex m dimensional vector space endowed nondegenerate orthogonal form here state prove formula giving schubert class decomposition cohomology products * general schubert classes special schubert classes chern classes dual tautological vector bundle rank discuss related properties reduced decompositions barred permutations even numbers bars divided differences associated even orthogonal group

Piotr Pragacz  1   ; Jan Ratajski  2

1 Institute of Mathematics Polish Academy of Sciences /Sniadeckich 8 P.O. Box 21 00-956 Warszawa 10, Poland
2 ING Nationale-Nederlanden Polska S.A. Ludna 2 00-406 Warszawa, Poland 
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Piotr Pragacz; Jan Ratajski. A Pieri-type formula for even orthogonal Grassmannians. Fundamenta Mathematicae, Tome 178 (2003) no. 1, pp. 49-96. doi: 10.4064/fm178-1-2

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