Homological realization of Nakajima varieties and Weyl group actions

Compositio Mathematica

Volumn 141, Issue 6, 2005, Pages 1479-1503

  Frenkel, Igor ^a   Khovanov, Mikhail ^b   Schiffmann, Olivier ^a,c  

^a YALE UNIVERSITY   (United States)

^b UNIVERSITY OF CALIFORNIA   (United States)

^c ÉCOLE NORMALE SUPÉRIEURE   (France)

Author keywords

Koszul duality; Nakajima quivers varieties; Weyl group

Indexed keywords

EID: 34347273789     PISSN: 0010437X     EISSN: None     Source Type: Journal    
DOI: 10.1112/S0010437X05001727     Document Type: Article

References (18)

1. n and problems of linear algebra, Funktsional. Anal., i Prilozhen. 12 (1978), 66-67 (in Russian).
2. 2, Compositio Math. 134 (2002), 283-318.
3. A. Beilinson, V. Ginzburg and W. Soergel, Koszul duality patterns in representation theory, J. Amer. Math. Soc. 9 (1996), 473-527.
4. R. Borcherds, Generalized Kac-Moody algebras, J. Algebra 115 (1988), 501-512.
5. W. Crawley-Boevey and M. Holland, Noncommutative deformations of Kleinian singularities, Duke Math. J. 92 (1998), 605-635.
6. D. Happel, Triangulated categories in the representation theory of finite-dimensional algebras, London Mathematical Society Lecture Note Series, vol. 119 (Cambridge University Press, Cambridge, 1988).
7. R. S. Huerfano and M. Khovanov, A category for the adjoint representation, J. Algebra 246 (2001), 514-542.
8. M. Khovanov and P. Seidel, Quivers, Floer cohomology, and braid group actions, J. Amer. Math. Soc. 15 (2002), 203-271.
9. S. Kurnar, Kac-Moody groups, their flag varieties and representation theory (Birkhäuser, Boston, MA, 2002).
10. G. Lusztig, Quiver varieties and Weyl group actions, Ann. Inst. Fourier (Grenoble) 50 (2000), 461-489.
11. A. Maffei, A remark on quiver varieties and Weyl groups, Ann. Sc. Norm. Super. Pisa Cl. Sci. (5) 1 (2002), 649-686.
12. D. McDuff and D. Salamon, J-holomorphic curves and quantum cohomology, University Lecture Series, vol. 6 (American Mathematical Society, Providence, RI, 1994).
13. H. Nakajima, Instantons on ALE spaces, quiver varieties, and Kac-Moody algebras, Duke Math. J. 76 (1994), 365-416.
14. H. Nakajima, Lectures on Hilbert schemes of points on surfaces, University Lecture Series, vol. 18 (American Mathematical Society, Providence, RI, 1999).
15. H. Nakajima, Reflection functors for quiver varieties and Weyl group actions, Math. Ann. 327 (2003), 671-721.
16. L. Peng and J. Xiao, Triangulated categories and Kac-Moody algebras, Invent. Math. 140 (2000), 563-603.
17. R. Rouquier and A. Zimmermann, Picard groups for derived module categories, Proc. London Math. Soc. (3) 87 (2003), 197-225.
18. P. Seidel and R. Thomas, Braid group actions on derived categories of coherent sheaves, Duke Math. J. 108 (2001), 37-108.