Quantization of the Marsden-Weinstein reduction for extended Dynkin quivers
Holland, Martin P.
Annales scientifiques de l'École Normale Supérieure, Tome 32 (1999), p. 813-834 / Harvested from Numdam
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@article{ASENS_1999_4_32_6_813_0,
     author = {Holland, Martin P.},
     title = {Quantization of the Marsden-Weinstein reduction for extended Dynkin quivers},
     journal = {Annales scientifiques de l'\'Ecole Normale Sup\'erieure},
     volume = {32},
     year = {1999},
     pages = {813-834},
     doi = {10.1016/s0012-9593(00)87719-8},
     mrnumber = {2001a:16042},
     zbl = {01383481},
     language = {en},
     url = {http://dml.mathdoc.fr/item/ASENS_1999_4_32_6_813_0}
}

Holland, Martin P. Quantization of the Marsden-Weinstein reduction for extended Dynkin quivers. Annales scientifiques de l'École Normale Supérieure, Tome 32 (1999) pp. 813-834. doi : 10.1016/s0012-9593(00)87719-8. http://gdmltest.u-ga.fr/item/ASENS_1999_4_32_6_813_0/

[1] A. Altman and S. Kleiman, Introduction to Grothendieck duality theory, Lect. Notes in Math., Vol. 146, 1970, Springer. | MR 43 #224 | Zbl 0215.37201

[2] D. Baer, W. Geigle and H. Lenzing, The preprojective algebra of a tame hereditary algebra, Comm. Algebra, Vol. 15, 1987, pp. 425-457. | MR 88i:16036 | Zbl 0612.16015

[3] A. Beilinson and J.N. Bernstein, Localisation de g-modules, C.R. Acad. Sci. Sér A-B, Vol. 292, 1981, pp. 15-18. | MR 82k:14015 | Zbl 0476.14019

[4] J.-E. Björk, Rings of differential operators, North-Holland, 1979. | Zbl 0499.13009

[5] W. Borho and J.-L. Brylinski, Differential operators on homogeneous spaces I, Invent. Math., Vol. 69, 1982, pp. 437-476. | MR 84b:17007 | Zbl 0504.22015

[6] W. Crawley-Boevey, Geometry of the moment map for representations of quivers, preprint, 1998.

[7] W. Crawley-Boevey, Preprojective algebras, differential operators and a Conze embedding for deformations of Kleinian singularities, preprint, 1998.

[8] W. Crawley-Boevey and M.P. Holland, Noncommutative deformations of Kleinian singularities, Duke Math. J., Vol. 92, 1998, pp. 605-635. | MR 99f:14003 | Zbl 0974.16007

[9] V. Dlab and C.M. Ringel, The preprojective algebra of a modulated graph. In : Representation theory II, Proc. Ottawa 1979, eds V. Dlab and P. Gabriel, Lec. Notes in Math., Vol. 832, Springer, 1980, pp. 216-231. | MR 83c:16022 | Zbl 0489.16024

[10] A. Grothendieck, Eléments de géométrie algébrique IV, Publ. Math. IHES, Vol. 28, 1966. | Numdam | Zbl 0144.19904

[11] R. Hartshorne, Algebraic Geometry, Graduate Texts in Math., Vol. 52, Springer, 1983. | MR 57 #3116 | Zbl 0531.14001

[12] T.J. Hodges and S.P. Smith, Rings of differential operators and the Beilinson-Bernstein equivalence of categories, Proc. Amer. Math. Soc., Vol. 93, 1985, pp. 379-386. | MR 86j:17015 | Zbl 0566.14011

[13] V.G. Kac, Some remarks on representations of quivers and infinite root systems. In : Representation theory II, Proc. Ottawa 1979, eds V. Dlab and P. Gabriel, Lect. Notes in Math., Vol. 832, Springer, 1980, pp. 311-327. | MR 82j:16051 | Zbl 0471.16023

[14] A.D. King, Moduli of representations of finite dimensional algebras, Quart. J. Math. Oxford, Vol. 45, 1994, pp. 515-530. | MR 96a:16009 | Zbl 0837.16005

[15] F. Knop, A Harish-Chandra homomorphism for reductive group actions, Ann. of Math., Vol. 140, 1994, pp. 253-288. | MR 95h:14045 | Zbl 0828.22017

[16] P.B. Kronheimer, The construction of ALE spaces as hyper-Kähler quotients, J. Diff. Geom., Vol. 29, 1989, pp. 665-683. | MR 90d:53055 | Zbl 0671.53045

[17] L. Le Bruyn and C. Procesi, Semisimple representations of quivers, Trans. Amer. Math. Soc., Vol. 317, 1990, pp. 585-598. | MR 90e:16048 | Zbl 0693.16018

[18] T. Levasseur, Relèvements d'opérateurs différentiels sur les anneaux d'invariants. In Operator Algebras, Unitary Representations, Enveloping Algebras and Invariant Theory, Progress in Math., Vol. 92, Birkhaüser, 1990, pp. 449-470. | MR 92f:16033 | Zbl 0733.16009

[19] T. Levasseur and J.T. Stafford, Rings of differential operators on classical rings of invariants, Memoirs of the AMS, Vol. 412, 1989. | MR 90i:17018 | Zbl 0691.16019

[20] G. Lusztig, Quivers, perverse sheaves and quantized enveloping algebras, J. Amer. Math. Soc., Vol. 4, 1991, pp. 365-421. | MR 91m:17018 | Zbl 0738.17011

[21] J.C. Mcconnell and J.C. Robson, Noncommutative Noetherian rings, Wiley, 1988. | Zbl 0644.16008

[22] J.C. Mcconnell and J.T. Stafford, Gelfand-Kirillov dimension and associated graded modules, J. Algebra, Vol. 125, 1989, pp. 197-214. | MR 90i:16002 | Zbl 0688.16030

[23] J. Mckay, Graphs, singularities and finite groups, Proc. Symp. Pure Math., Vol. 37, 1980, pp. 183-186. | MR 82e:20014 | Zbl 0451.05026

[24] D. Mumford, J. Fogarty and F. Kirwan, Geometric Invariant Theory, Third edition, Springer 1994. | MR 95m:14012 | Zbl 0797.14004

[25] I. Musson, Rings of differential operators on invariant rings of tori, Trans. Amer. Math. Soc., Vol. 303, 1987, pp. 805-827. | MR 88m:32019 | Zbl 0628.13019

[26] I. Musson and M. Van Den Bergh, Invariants under tori of rings of differential operators and related topics, preprint. | Zbl 0928.16019

[27] H. Nakajima, Instantons on ALE spaces, quiver varieties, and Kac-Moody algebras, Duke Math. J., Vol. 76, 1994, pp. 365-416. | MR 95i:53051 | Zbl 0826.17026

[28] H. Nakajima, Varieties associated with quivers. In Representation theory of algebras and related topics, eds R. Bautista et al., Canadian Math. Soc. Conf. Proc., Amer. Math. Soc., Vol. 19, 1996. | MR 97m:16022 | Zbl 0870.16008

[29] C.M. Ringel, The rational invariants of the tame quivers, Invent. Math., Vol. 58, 1980, pp. 217-239. | MR 81f:16048 | Zbl 0433.15009

[30] G.W. Schwarz, Lifting differential operators from orbit spaces, Ann. Sci. Éc. Norm. Sup., t. 28, 1995, pp. 253-305. | Numdam | MR 96f:14061 | Zbl 0836.14032

[31] G.W. Schwarz, Differential operators on quotients of simple groups, J. Algebra, Vol. 169, 1994, pp. 248-273. | MR 95i:16027 | Zbl 0835.14019

[32] M. Van Den Bergh, Differential operators on semi-invariants for tori and weighted projective spaces, Topics in invariant theory (M. P. Malliavin ed.), Lect. Notes in Math., Vol. 1478, Springer Verlag, 1991, pp. 255-272. | MR 93h:16046 | Zbl 0802.13005

[33] C.A. Weibel, An introduction to homological algebra, C.U.P., 1994. | MR 95f:18001 | Zbl 0797.18001