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ArticleOriginal scientific text

Title

Twisted action of the symmetric group on the cohomology of a flag manifold

Authors 1, 1, 2

Affiliations

  1. L.I.T.P., Université Paris 7, 2, Place Jussieu, 75251 Paris Cedex 05, France
  2. Institut Gaspard Monge, Université de Marne-la-Vallée, 2, rue de la Butte-Verte, 93166 Noisy-le-Grand Cedex, France

Abstract

Classes dual to Schubert cycles constitute a basis on the cohomology ring of the flag manifold F, self-adjoint up to indexation with respect to the intersection form. Here, we study the bilinear form (X,Y) :=〈X·Y, c(F)〉 where X,Y are cocycles, c(F) is the total Chern class of F and〈,〉 is the intersection form. This form is related to a twisted action of the symmetric group of the cohomology ring, and to the degenerate affine Hecke algebra. We give a distinguished basis for this form, which is a deformation of the usual basis of Schubert polynomials, and apply it to the computation of the Schubert cycle expansions of Chern classes of flag manifolds.

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Banach Center Publications
1996/36/1
Export to PBN, Opens in new tab
Pages:
111-124
Main language of publication
English
Published
1996
Exact and natural sciences