A Pieri-type formula for even orthogonal Grassmannians

• Autorzy: Piotr Pragacz , Jan Ratajski
• Języki publikacji: EN

Abstrakty

EN

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).

Kategorie tematyczne

• 14M15: Grassmannians, Schubert varieties, flag manifolds
• 05E05: Symmetric functions and generalizations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2003
• Tom: 178
• Numer: 1
• Strony: 49-96

Daty

wydano

2003

Twórcy

autor

Piotr Pragacz

• Institute of Mathematics, Polish Academy of Sciences, Śniadeckich 8, P.O. Box 21, 00-956 Warszawa 10, Poland

autor

Jan Ratajski

• ING Nationale-Nederlanden Polska S.A., Ludna 2, 00-406 Warszawa, Poland

Identyfikatory

DOI

10.4064/fm178-1-2