PL EN


Preferencje help
Widoczny [Schowaj] Abstrakt
Liczba wyników
1996 | 36 | 1 | 111-124
Tytuł artykułu

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

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
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.
Słowa kluczowe
Rocznik
Tom
36
Numer
1
Strony
111-124
Opis fizyczny
Daty
wydano
1996
Twórcy
  • L.I.T.P., Université Paris 7, 2, Place Jussieu, 75251 Paris Cedex 05, France
  • L.I.T.P., Université Paris 7, 2, Place Jussieu, 75251 Paris Cedex 05, France
  • Institut Gaspard Monge, Université de Marne-la-Vallée, 2, rue de la Butte-Verte, 93166 Noisy-le-Grand Cedex, France
Bibliografia
  • [1] I. N. Bernstein, I. M. Gelfand and S. I. Gelfand, Schubert cells and the cohomology of the spaces G/P, Russian Math. Surveys 28 (1973), 1-26.
  • [2] I. V. Cherednik, On R-matrix quantization of formal loop groups, in: Group theoretical methods in physics, Vol. II (Yurmala, 1985), 161-180, VNU Sci. Press, Utrecht, 1986.
  • [3] I. V. Cherednik, Quantum groups as hidden symmetries of classic representation theory, in: Differential geometric methods in theoretical physics (A. I. Solomon ed.), World Scientific, Singapore, 1989, 47-54.
  • [4] M. Demazure, Désingularisation des variétés de Schubert généralisées, Ann. Sci. École Norm. Sup. (4) 7 (1974), 53-88.
  • [5] M. Demazure, Invariants symétriques entiers des groupes de Weyl et torsion, Invent. Math. 21 (1973), 287-301.
  • [6] G. Duchamp, D. Krob, A. Lascoux, B. Leclerc, T. Scharf and J.-Y. Thibon, Euler-Poincaré characteristic and polynomial representations of Iwahori-Hecke algebras, Publ. Res. Inst. Math. Sci. 31 (1995), 179-201.
  • [7] W. Fulton, Schubert varieties in flag bundles for the Classical Groups, preprint, University of Chicago, 1994; to appear in: Proceedings of the Conference in Honor of Hirzebruch's 65th Birthday, Bar Ilan, 1993.
  • [8] F. Hirzebruch, Topological methods in algebraic geometry, Springer, Berlin, 1966.
  • [9] A. Kerber, A. Kohnert and A. Lascoux, SYMMETRICA, an object oriented computer algebra system for the symmetric group, J. Symbolic Comput. 14 (1992), 195-203.
  • [10] A. Lascoux, Classes de Chern des variétés de drapeaux, C. R. Acad. Sci. Paris Sér. I Math. 295 (1982), 393-398.
  • [11] A. Lascoux and M.-P. Schützenberger, Polynômes de Schubert, C. R. Acad. Sci. Paris Sér. I Math. 294 (1982), 447-450.
  • [12] A. Lascoux and M.-P. Schützenberger, Symmetrization operators on polynomial rings, Functional Anal. Appl. 21 (1987), 77-78.
  • [13] G. Lusztig, Equivariant K-theory and representations of Hecke Algebras, Proc. Amer. Math. Soc. 94 (1985), 337-342.
  • [14] I. G. Macdonald, Notes on Schubert polynomials, Publ. LACIM 6, UQAM, Montréal, 1991.
  • [15] P. Pragacz and J. Ratajski, Formulas for Lagrangian and orthogonal degeneracy loci: the $\tilde Q$-polynomials approach, Max-Planck-Institut für Mathematik Preprint 1994; to appear in Compositio Math.
  • [16] S. Veigneau, SP, a Maple package for Schubert polynomials, Université de Marne-la-Vallée, 1994.
  • [17] C. N. Yang, Some exact results for the many-body problem in one dimension with repulsive delta-function interaction, Phys. Rev. Lett. 19 (1967), 1312-1315.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-bcpv36z1p111bwm
JavaScript jest wyłączony w Twojej przeglądarce internetowej. Włącz go, a następnie odśwież stronę, aby móc w pełni z niej korzystać.