Quiver varieties and Weyl group actions

George Lusztig

Annales de l'institut Fourier (2000)

  • Volume: 50, Issue: 2, page 461-489
  • ISSN: 0373-0956

Abstract

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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.

How to cite

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Lusztig, George. "Quiver varieties and Weyl group actions." Annales de l'institut Fourier 50.2 (2000): 461-489. <http://eudml.org/doc/75426>.

@article{Lusztig2000,
abstract = {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.},
author = {Lusztig, George},
journal = {Annales de l'institut Fourier},
keywords = {quiver varieties; Weyl groups; intersection cohomology; Weyl group actions},
language = {eng},
number = {2},
pages = {461-489},
publisher = {Association des Annales de l'Institut Fourier},
title = {Quiver varieties and Weyl group actions},
url = {http://eudml.org/doc/75426},
volume = {50},
year = {2000},
}

TY - JOUR
AU - Lusztig, George
TI - Quiver varieties and Weyl group actions
JO - Annales de l'institut Fourier
PY - 2000
PB - Association des Annales de l'Institut Fourier
VL - 50
IS - 2
SP - 461
EP - 489
AB - 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.
LA - eng
KW - quiver varieties; Weyl groups; intersection cohomology; Weyl group actions
UR - http://eudml.org/doc/75426
ER -

References

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  1. [L1] G. LUSZTIG, Green polynomials and singularities of unipotent classes, Adv. in Math., 42 (1981), 169-178. Zbl0473.20029MR83c:20059
  2. [L2] G. LUSZTIG, Cuspidal local systems and representations of graded Hecke algebras, I, Publ. Math. IHES, 67 (1988), 145-202. Zbl0699.22026MR90e:22029
  3. [L3] G. LUSZTIG, Quivers, perverse sheaves and enveloping algebras, J. Amer. Math. Soc., 4 (1991), 365-421. Zbl0738.17011MR91m:17018
  4. [L4] G. LUSZTIG, On quiver varieties, Adv. in Math., 136 (1998), 141-182. Zbl0915.17008MR2000c:16016
  5. [N1] H. NAKAJIMA, Instantons on ALE spaces, quiver varieties and Kac-Moody algebras, Duke J. Math., 76 (1994), 365-416. Zbl0826.17026MR95i:53051
  6. [N2] H. NAKAJIMA, Quiver varieties and Kac-Moody algebras, Duke J. Math., 91 (1998), 515-560. Zbl0970.17017MR99b:17033

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