A Pieri-type formula for even orthogonal Grassmannians
Fundamenta Mathematicae, Tome 178 (2003) no. 1, p. 49.

Voir la notice de l'article dans European Digital Mathematics Library

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).
Classification : 14F20, 05E15, 14M15, 14N15, 51M35
Mots-clés : cohomology ring, Grassmannians, Schubert classes, isotropic subspaces, Pieri-type formulas 
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Piotr Pragacz; Jan Ratajski. A Pieri-type formula for even orthogonal Grassmannians. Fundamenta Mathematicae, Tome 178 (2003) no. 1, p. 49. https://geodesic-test.mathdoc.fr/item/FUNDAM_2003__178_1_283362/