Quiver varieties and Weyl group actions
Annales de l'Institut Fourier, Volume 50 (2000) no. 2, pp. 461-489.

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.

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.

@article{AIF_2000__50_2_461_0,
     author = {Lusztig, George},
     title = {Quiver varieties and {Weyl} group actions},
     journal = {Annales de l'Institut Fourier},
     pages = {461--489},
     publisher = {Association des Annales de l{\textquoteright}institut Fourier},
     volume = {50},
     number = {2},
     year = {2000},
     doi = {10.5802/aif.1762},
     mrnumber = {1775358},
     zbl = {0958.20036},
     language = {en},
     url = {http://www.numdam.org/articles/10.5802/aif.1762/}
}
TY  - JOUR
AU  - Lusztig, George
TI  - Quiver varieties and Weyl group actions
JO  - Annales de l'Institut Fourier
PY  - 2000
DA  - 2000///
SP  - 461
EP  - 489
VL  - 50
IS  - 2
PB  - Association des Annales de l’institut Fourier
UR  - http://www.numdam.org/articles/10.5802/aif.1762/
UR  - https://www.ams.org/mathscinet-getitem?mr=1775358
UR  - https://zbmath.org/?q=an%3A0958.20036
UR  - https://doi.org/10.5802/aif.1762
DO  - 10.5802/aif.1762
LA  - en
ID  - AIF_2000__50_2_461_0
ER  - 
%0 Journal Article
%A Lusztig, George
%T Quiver varieties and Weyl group actions
%J Annales de l'Institut Fourier
%D 2000
%P 461-489
%V 50
%N 2
%I Association des Annales de l’institut Fourier
%U https://doi.org/10.5802/aif.1762
%R 10.5802/aif.1762
%G en
%F AIF_2000__50_2_461_0
Lusztig, George. Quiver varieties and Weyl group actions. Annales de l'Institut Fourier, Volume 50 (2000) no. 2, pp. 461-489. doi : 10.5802/aif.1762. http://www.numdam.org/articles/10.5802/aif.1762/

[L1] G. Lusztig, Green polynomials and singularities of unipotent classes, Adv. in Math., 42 (1981), 169-178. | MR | Zbl

[L2] G. Lusztig, Cuspidal local systems and representations of graded Hecke algebras, I, Publ. Math. IHES, 67 (1988), 145-202. | Numdam | MR | Zbl

[L3] G. Lusztig, Quivers, perverse sheaves and enveloping algebras, J. Amer. Math. Soc., 4 (1991), 365-421. | MR | Zbl

[L4] G. Lusztig, On quiver varieties, Adv. in Math., 136 (1998), 141-182. | MR | Zbl

[N1] H. Nakajima, Instantons on ALE spaces, quiver varieties and Kac-Moody algebras, Duke J. Math., 76 (1994), 365-416. | MR | Zbl

[N2] H. Nakajima, Quiver varieties and Kac-Moody algebras, Duke J. Math., 91 (1998), 515-560. | MR | Zbl

Cited by Sources: