A remark on quiver varieties and Weyl groups

Andrea Maffei

Annali della Scuola Normale Superiore di Pisa - Classe di Scienze (2002)

  • Volume: 1, Issue: 3, page 649-686
  • ISSN: 0391-173X

Abstract

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In this paper we define an action of the Weyl group on the quiver varieties M m , λ ( v ) with generic ( m , λ ) .

How to cite

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Maffei, Andrea. "A remark on quiver varieties and Weyl groups." Annali della Scuola Normale Superiore di Pisa - Classe di Scienze 1.3 (2002): 649-686. <http://eudml.org/doc/84483>.

@article{Maffei2002,
abstract = {In this paper we define an action of the Weyl group on the quiver varieties $M_\{m, \lambda \}(v)$ with generic $(m, \lambda )$.},
author = {Maffei, Andrea},
journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
keywords = {action of Weyl group; projective ring; smooth quiver variety; quiver of finite type},
language = {eng},
number = {3},
pages = {649-686},
publisher = {Scuola normale superiore},
title = {A remark on quiver varieties and Weyl groups},
url = {http://eudml.org/doc/84483},
volume = {1},
year = {2002},
}

TY - JOUR
AU - Maffei, Andrea
TI - A remark on quiver varieties and Weyl groups
JO - Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
PY - 2002
PB - Scuola normale superiore
VL - 1
IS - 3
SP - 649
EP - 686
AB - In this paper we define an action of the Weyl group on the quiver varieties $M_{m, \lambda }(v)$ with generic $(m, \lambda )$.
LA - eng
KW - action of Weyl group; projective ring; smooth quiver variety; quiver of finite type
UR - http://eudml.org/doc/84483
ER -

References

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  1. [1] L. Le Bruyn – C. Procesi, Semisimple representations of quivers, Trans. Amer. Math. Soc. 317 (1990), 585-598. Zbl0693.16018MR958897
  2. [2] W. Crawley-Boevey, Geometry of the moment map for representations of quivers, preprint available at http://www.amsta.leeds.ac.uk/~pmtwc. Zbl1037.16007MR1834739
  3. [3] H. Derksen – J. Weyman, Semi-invariants of quivers and saturation for Littlewood-Richardson coefficients, J. Amer. Math. Soc. 13 (2000), 467-479. Zbl0993.16011MR1758750
  4. [4] G. Kempf – L. Ness, The length of vectors in representation spaces, In: “Algebraic geometry”. Proc. Summer Meeting Univ. Copenhagen 1978, Vol. 732 of LNM, Springer, 1979, pp. 233-243. Zbl0407.22012MR555701
  5. [5] G. Lusztig, On quiver varieties, Adv. Math. 136 (1998), 141-182. Zbl0915.17008MR1623674
  6. [6] G. Lusztig, Quiver varieties and Weyl group actions, Ann. Inst. Fourier (Grenoble) 50 (2000), 461-489. Zbl0958.20036MR1775358
  7. [7] A. Maffei, A remark on quiver varieties and Weyl groups, preprint available at http://xxx.lanl.gov. Zbl1143.14309
  8. [8] A. Maffei, “Quiver varieties”, PhD thesis, Università di Roma “La Sapienza", 1999. 
  9. [9] L. Migliorini, Stability of homogeneous vector bundles, Boll. Un. Mat. Ital. 7-B (1996), 963-990. Zbl0885.14024MR1430162
  10. [10] D. Mumford – J. Fogarty – F. Kirwan, “Geometric invariant theory”, Ergebn. der Math., Vol. 34, Springer, third edition, 1994. Zbl0797.14004MR1304906
  11. [11] H. Nakajima, Instantons on ALE spaces, quiver varieties, and Kac-Moody algebras, Duke Math. J. 76 (1994), 365-416. Zbl0826.17026MR1302318
  12. [12] H. Nakajima, Quiver varieties and Kac-Moody algebras, Duke Math. J. 91 (1998), 515-560. Zbl0970.17017MR1604167
  13. [13] P. Newstead, “Introduction to moduli problems and orbit spaces”, Tata Lectures, Vol. 51, Springer, 1978. Zbl0411.14003MR546290

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