Il est connu que le groupe de Weyl opère naturellement sur la cohomologie d’une variété de Nakajima. Ici ce fait est établi en utilisant la méthode de la cohomologie d’intersection, en analogie avec la définition des représentations de Springer.
The cohomology of Nakajima’s varieties is known to carry a natural Weyl group action. Here this fact is established using the method of intersection cohomology, in analogy with the definition of Springer’s representations.
@article{AIF_2000__50_2_461_0,
author = {Lusztig, George},
title = {Quiver varieties and Weyl group actions},
journal = {Annales de l'Institut Fourier},
volume = {50},
year = {2000},
pages = {461-489},
doi = {10.5802/aif.1762},
mrnumber = {2001h:17031},
zbl = {0958.20036},
mrnumber = {1775358},
language = {en},
url = {http://dml.mathdoc.fr/item/AIF_2000__50_2_461_0}
}
Lusztig, George. Quiver varieties and Weyl group actions. Annales de l'Institut Fourier, Tome 50 (2000) pp. 461-489. doi : 10.5802/aif.1762. http://gdmltest.u-ga.fr/item/AIF_2000__50_2_461_0/
[L1] , Green polynomials and singularities of unipotent classes, Adv. in Math., 42 (1981), 169-178. | MR 83c:20059 | Zbl 0473.20029
[L2] , Cuspidal local systems and representations of graded Hecke algebras, I, Publ. Math. IHES, 67 (1988), 145-202. | Numdam | MR 90e:22029 | Zbl 0699.22026
[L3] , Quivers, perverse sheaves and enveloping algebras, J. Amer. Math. Soc., 4 (1991), 365-421. | MR 91m:17018 | Zbl 0738.17011
[L4] , On quiver varieties, Adv. in Math., 136 (1998), 141-182. | MR 2000c:16016 | Zbl 0915.17008
[N1] , Instantons on ALE spaces, quiver varieties and Kac-Moody algebras, Duke J. Math., 76 (1994), 365-416. | MR 95i:53051 | Zbl 0826.17026
[N2] , Quiver varieties and Kac-Moody algebras, Duke J. Math., 91 (1998), 515-560. | MR 99b:17033 | Zbl 0970.17017