A Pieri-type formula for even orthogonal Grassmannians
Tom 178 / 2003
Fundamenta Mathematicae 178 (2003), 49-96
MSC: 14M15, 05E05.
DOI: 10.4064/fm178-1-2
Streszczenie
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 $SO(2m)$.