A Pieri-type formula for even orthogonal Grassmannians

Piotr Pragacz; Jan Ratajski

Fundamenta Mathematicae (2003)

  • Volume: 178, Issue: 1, page 49-96
  • ISSN: 0016-2736

Abstract

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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 ≤ 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).

How to cite

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Piotr Pragacz, and Jan Ratajski. "A Pieri-type formula for even orthogonal Grassmannians." Fundamenta Mathematicae 178.1 (2003): 49-96. <http://eudml.org/doc/283362>.

@article{PiotrPragacz2003,
abstract = {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 ≤ 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).},
author = {Piotr Pragacz, Jan Ratajski},
journal = {Fundamenta Mathematicae},
keywords = {cohomology ring; Grassmannians; Schubert classes; isotropic subspaces; Pieri-type formulas},
language = {eng},
number = {1},
pages = {49-96},
title = {A Pieri-type formula for even orthogonal Grassmannians},
url = {http://eudml.org/doc/283362},
volume = {178},
year = {2003},
}

TY - JOUR
AU - Piotr Pragacz
AU - Jan Ratajski
TI - A Pieri-type formula for even orthogonal Grassmannians
JO - Fundamenta Mathematicae
PY - 2003
VL - 178
IS - 1
SP - 49
EP - 96
AB - 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 ≤ 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).
LA - eng
KW - cohomology ring; Grassmannians; Schubert classes; isotropic subspaces; Pieri-type formulas
UR - http://eudml.org/doc/283362
ER -

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