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

Alain Lascoux; Bernard Leclerc; Jean-Yves Thibon

Banach Center Publications (1996)

- Volume: 36, Issue: 1, page 111-124
- ISSN: 0137-6934

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topLascoux, Alain, Leclerc, Bernard, and Thibon, Jean-Yves. "Twisted action of the symmetric group on the cohomology of a flag manifold." Banach Center Publications 36.1 (1996): 111-124. <http://eudml.org/doc/208575>.

@article{Lascoux1996,

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.},

author = {Lascoux, Alain, Leclerc, Bernard, Thibon, Jean-Yves},

journal = {Banach Center Publications},

keywords = {cohomology ring; action of the symmetric group; degenerate affine Hecke algebra; variety of complete flags; Schubert polynomials; Schubert cycles},

language = {eng},

number = {1},

pages = {111-124},

title = {Twisted action of the symmetric group on the cohomology of a flag manifold},

url = {http://eudml.org/doc/208575},

volume = {36},

year = {1996},

}

TY - JOUR

AU - Lascoux, Alain

AU - Leclerc, Bernard

AU - Thibon, Jean-Yves

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

JO - Banach Center Publications

PY - 1996

VL - 36

IS - 1

SP - 111

EP - 124

AB - 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.

LA - eng

KW - cohomology ring; action of the symmetric group; degenerate affine Hecke algebra; variety of complete flags; Schubert polynomials; Schubert cycles

UR - http://eudml.org/doc/208575

ER -

## References

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