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).
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm178-1-2,
author = {Piotr Pragacz and Jan Ratajski},
title = {A Pieri-type formula for even orthogonal Grassmannians},
journal = {Fundamenta Mathematicae},
volume = {177},
year = {2003},
pages = {49-96},
zbl = {1037.51012},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm178-1-2}
}
Piotr Pragacz; Jan Ratajski. A Pieri-type formula for even orthogonal Grassmannians. Fundamenta Mathematicae, Tome 177 (2003) pp. 49-96. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm178-1-2/