# Wydawnictwa / Banach Center Publications / Wszystkie tomy

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

### Tom 36 / 1996

Banach Center Publications 36 (1996), 111-124 DOI: 10.4064/-36-1-111-124

#### Streszczenie

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.

#### Autorzy

• Alain Lascoux
• Bernard Leclerc
• Jean-Yves Thibon

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