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A Pieri-type formula for even orthogonal Grassmannians

Piotr Pragacz, Jan Ratajski (2003)

Fundamenta Mathematicae

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...

Sugli isomorfismi tra spazi di Grassman

Eva Ferrara Dentice, Nicola Melone (1999)

Bollettino dell'Unione Matematica Italiana

In this paper we prove that any incidence-preserving bijection between the line sets of Grassmann spaces is induced by either a collineation or a correlation.

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