Instantons on ALE spaces, quiver varieties, and Kac-Moody algebras

previous :: next

Instantons on ALE spaces, quiver varieties, and Kac-Moody algebras

Hiraku Nakajima

Source: Duke Math. J. Volume 76, Number 2 (1994), 365-416.

First Page: Show

Primary Subjects: 53C25

Secondary Subjects: 17B67, 58D27, 58E15

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber.

If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Links and Identifiers

Permanent link to this document: http://projecteuclid.org/euclid.dmj/1077286968
Mathematical Reviews number (MathSciNet): MR1302318
Zentralblatt MATH identifier: 0826.17026
Digital Object Identifier: doi:10.1215/S0012-7094-94-07613-8

back to Table of Contents

References

[At] M. F. Atiyah, Convexity and commuting Hamiltonians, Bull. London Math. Soc. 14 (1982), no. 1, 1–15.

Mathematical Reviews (MathSciNet): MR83e:53037

Zentralblatt MATH: 0482.58013

Digital Object Identifier: doi:10.1112/blms/14.1.1

[AB] M. F. Atiyah and R. Bott, The Yang-Mills equations over Riemann surfaces, Philos. Trans. Roy. Soc. London Ser. A. 362 (1982), 523–615.

Zentralblatt MATH: 0509.14014

Mathematical Reviews (MathSciNet): MR702806

Digital Object Identifier: doi:10.1098/rsta.1983.0017

JSTOR: links.jstor.org

[ADHM] M. F. Atiyah, N. J. Hitchin, V. G. Drinfeld, and Yu. I. Manin, Construction of instantons, Phys. Lett. A 65 (1978), no. 3, 185–187.

Mathematical Reviews (MathSciNet): MR82g:81049

Zentralblatt MATH: 0424.14004

Digital Object Identifier: doi:10.1016/0375-9601(78)90141-X

[Ba] S. Bando, Einstein-Hermitian metrics on noncompact Kähler manifolds, Einstein metrics and Yang-Mills connections (Sanda, 1990) eds. T. Mabuchi and S. Mukai, Lecture Notes in Pure and Appl. Math., vol. 145, Dekker, New York, 1993, pp. 27–33.

Mathematical Reviews (MathSciNet): MR94d:32040

Zentralblatt MATH: 0809.53071

[BLM] A. Beilinson, G. Lusztig, and R. MacPherson, A geometric setting for the quantum deformation of $\rm GL\sb n$, Duke Math. J. 61 (1990), no. 2, 655–677.

Mathematical Reviews (MathSciNet): MR91m:17012

Zentralblatt MATH: 0713.17012

Digital Object Identifier: doi:10.1215/S0012-7094-90-06124-1

Project Euclid: euclid.dmj/1077296831

[BM] W. Borho and R. MacPherson, Partial resolutions of nilpotent varieties, Analysis and topology on singular spaces, II, III (Luminy, 1981), Astérisque, vol. 101, Soc. Math. France, Paris, 1983, pp. 23–74.

Mathematical Reviews (MathSciNet): MR85j:14087

Zentralblatt MATH: 0576.14046

[Bo] R. Bott, Nondegenerate critical manifolds, Ann. of Math. (2) 60 (1954), 248–261.

Mathematical Reviews (MathSciNet): MR16,276f

Zentralblatt MATH: 0058.09101

Digital Object Identifier: doi:10.2307/1969631

JSTOR: links.jstor.org

[Do] S. K. Donaldson, Instantons and geometric invariant theory, Comm. Math. Phys. 93 (1984), no. 4, 453–460.

Mathematical Reviews (MathSciNet): MR86m:32043

Zentralblatt MATH: 0581.14008

Digital Object Identifier: doi:10.1007/BF01212289

Project Euclid: euclid.cmp/1103941177

[DK] S. K. Donaldson and P. B. Kronheimer, The geometry of four-manifolds, Oxford Mathematical Monographs, The Clarendon Press Oxford University Press, New York, 1990.

Mathematical Reviews (MathSciNet): MR92a:57036

Zentralblatt MATH: 0820.57002

[Fr] T. Frankel, Fixed points and torsion on Kähler manifolds, Ann. of Math. (2) 70 (1959), 1–8.

Mathematical Reviews (MathSciNet): MR24:A1730

Zentralblatt MATH: 0088.38002

Digital Object Identifier: doi:10.2307/1969889

[Ga] P. Gabriel, Unzerlegbare Darstellungen. I, Manuscripta Math. 6 (1972), 71–103.

Mathematical Reviews (MathSciNet): MR48:11212

Zentralblatt MATH: 0232.08001

Digital Object Identifier: doi:10.1007/BF01298413

[Gi] V. Ginzburg, Lagrangian construction of the enveloping algebra $U(\rm sl\sb n)$, C. R. Acad. Sci. Paris Sér. I Math. 312 (1991), no. 12, 907–912.

Mathematical Reviews (MathSciNet): MR92c:17017

Zentralblatt MATH: 0749.17009

[GN] T. Gocho and H. Nakajima, Einstein-Hermitian connections on hyper-Kähler quotients, J. Math. Soc. Japan 44 (1992), no. 1, 43–51.

Mathematical Reviews (MathSciNet): MR92k:53079

Zentralblatt MATH: 0767.53045

Digital Object Identifier: doi:10.2969/jmsj/04410043

Project Euclid: euclid.jmsj/1227107863

[Go] R. Goto, On toric hyper-Kähler manifolds given by the hyper-Kähler quotient method, Infinite analysis, Part A, B (Kyoto, 1991), Adv. Ser. Math. Phys., vol. 16, World Sci. Publishing, River Edge, NJ, 1992, pp. 317–338.

Mathematical Reviews (MathSciNet): MR93m:53040

Zentralblatt MATH: 0924.53023

[Hi] N. J. Hitchin, The self-duality equations on a Riemann surface, Proc. London Math. Soc. (3) 55 (1987), no. 1, 59–126.

Mathematical Reviews (MathSciNet): MR89a:32021

Zentralblatt MATH: 0634.53045

Digital Object Identifier: doi:10.1112/plms/s3-55.1.59

[HKLR] N. J. Hitchin, A. Karlhede, U. Lindström, and M. Roček, Hyper-Kähler metrics and supersymmetry, Comm. Math. Phys. 108 (1987), no. 4, 535–589.

Mathematical Reviews (MathSciNet): MR88g:53048

Zentralblatt MATH: 0612.53043

Digital Object Identifier: doi:10.1007/BF01214418

Project Euclid: euclid.cmp/1104116624

[Kac] V. G. Kac, Infinite-dimensional Lie algebras, Cambridge University Press, Cambridge, 1990.

Mathematical Reviews (MathSciNet): MR92k:17038

Zentralblatt MATH: 0716.17022

[KS] M. Kashiwara and P. Schapira, Sheaves on manifolds, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 292, Springer-Verlag, Berlin, 1990.

Mathematical Reviews (MathSciNet): MR92a:58132

Zentralblatt MATH: 0709.18001

[Kin] A. D. King, Moduli of representations of finite dimensional algebras, to appear in Quart. J. Math. Oxford Ser. (2).

Mathematical Reviews (MathSciNet): MR1315461

Zentralblatt MATH: 0837.16005

Digital Object Identifier: doi:10.1093/qmath/45.4.515

[Ki] F. C. Kirwan, Cohomology of quotients in symplectic and algebraic geometry, Mathematical Notes, vol. 31, Princeton University Press, Princeton, NJ, 1984.

Mathematical Reviews (MathSciNet): MR86i:58050

Zentralblatt MATH: 0553.14020

[KP] H. Kraft and C. Procesi, Closures of conjugacy classes of matrices are normal, Invent. Math. 53 (1979), no. 3, 227–247.

Mathematical Reviews (MathSciNet): MR80m:14037

Zentralblatt MATH: 0434.14026

Digital Object Identifier: doi:10.1007/BF01389764

[Kr1] P. B. Kronheimer, The construction of ALE spaces as hyper-Kähler quotients, J. Differential Geom. 29 (1989), no. 3, 665–683.

Mathematical Reviews (MathSciNet): MR90d:53055

Zentralblatt MATH: 0671.53045

Project Euclid: euclid.jdg/1214443066

[Kr2] P. B. Kronheimer, Instantons and the geometry of the nilpotent variety, J. Differential Geom. 32 (1990), no. 2, 473–490.

Mathematical Reviews (MathSciNet): MR91m:58021

Zentralblatt MATH: 0725.58007

Project Euclid: euclid.jdg/1214445316

[KN] P. B. Kronheimer and H. Nakajima, Yang-Mills instantons on ALE gravitational instantons, Math. Ann. 288 (1990), no. 2, 263–307.

Mathematical Reviews (MathSciNet): MR92e:58038

Zentralblatt MATH: 0694.53025

Digital Object Identifier: doi:10.1007/BF01444534

[La] G. Laumon, Correspondance de Langlands géométrique pour les corps de fonctions, Duke Math. J. 54 (1987), no. 2, 309–359.

Mathematical Reviews (MathSciNet): MR88g:11086

Zentralblatt MATH: 0662.12013

Digital Object Identifier: doi:10.1215/S0012-7094-87-05418-4

Project Euclid: euclid.dmj/1077305666

[L1] G. Lusztig, Quantum deformations of certain simple modules over enveloping algebras, Adv. in Math. 70 (1988), no. 2, 237–249.

Mathematical Reviews (MathSciNet): MR89k:17029

Zentralblatt MATH: 0651.17007

Digital Object Identifier: doi:10.1016/0001-8708(88)90056-4

[L2] G. Lusztig, Canonical bases arising from quantized enveloping algebras, J. Amer. Math. Soc. 3 (1990), no. 2, 447–498.

Mathematical Reviews (MathSciNet): MR90m:17023

Zentralblatt MATH: 0703.17008

Digital Object Identifier: doi:10.2307/1990961

JSTOR: links.jstor.org

[L3] G. Lusztig, Quivers, perverse sheaves, and quantized enveloping algebras, J. Amer. Math. Soc. 4 (1991), no. 2, 365–421.

Mathematical Reviews (MathSciNet): MR91m:17018

Zentralblatt MATH: 0738.17011

Digital Object Identifier: doi:10.2307/2939279

JSTOR: links.jstor.org

[L4] G. Lusztig, Affine quivers and canonical bases, Inst. Hautes Études Sci. Publ. Math. (1992), no. 76, 111–163.

Mathematical Reviews (MathSciNet): MR94h:16021

Zentralblatt MATH: 0776.17013

Digital Object Identifier: doi:10.1007/BF02699432

[Mc] R. D. MacPherson, Chern classes for singular algebraic varieties, Ann. of Math. (2) 100 (1974), 423–432.

Mathematical Reviews (MathSciNet): MR50:13587

Zentralblatt MATH: 0311.14001

Digital Object Identifier: doi:10.2307/1971080

JSTOR: links.jstor.org

[Na1] H. Nakajima, Moduli spaces of anti-self-dual connections on ALE gravitational instantons, Invent. Math. 102 (1990), no. 2, 267–303.

Mathematical Reviews (MathSciNet): MR92a:58024

Zentralblatt MATH: 0714.53026

Digital Object Identifier: doi:10.1007/BF01233429

[Na2] H. Nakajima, Homology of moduli spaces of instantons on ALE spaces (I), to appear in J. Differential Geom.

Mathematical Reviews (MathSciNet): MR1285530

Zentralblatt MATH: 0822.53019

Project Euclid: euclid.jdg/1214455288

[Na3] H. Nakajima, Resolutions of moduli spaces of ideal instantons on $\mathbbR^4$, proceedings of the 1993 Taniguchi Symposium on Low-dimensional Topology and Topological Field Theory, to appear.

[Na4] H. Nakajima, Gauge theory on resolutions of simple singularities and simple Lie algebras, Internat. Math. Res. Notices (1994), no. 2, 61–74.

Mathematical Reviews (MathSciNet): MR95j:53043

Zentralblatt MATH: 0832.58007

Digital Object Identifier: doi:10.1155/S1073792894000085

[Nee] A. Neeman, The topology of quotient varieties, Ann. of Math. (2) 122 (1985), no. 3, 419–459.

Mathematical Reviews (MathSciNet): MR87g:14010

Zentralblatt MATH: 0692.14032

Digital Object Identifier: doi:10.2307/1971309

JSTOR: links.jstor.org

[Ne] L. Ness, A stratification of the null cone via the moment map, Amer. J. Math. 106 (1984), no. 6, 1281–1329.

Mathematical Reviews (MathSciNet): MR86c:14010

Zentralblatt MATH: 0604.14006

Digital Object Identifier: doi:10.2307/2374395

JSTOR: links.jstor.org

[Ri] C. M. Ringel, Hall algebras and quantum groups, Invent. Math. 101 (1990), no. 3, 583–591.

Mathematical Reviews (MathSciNet): MR91i:16024

Zentralblatt MATH: 0735.16009

Digital Object Identifier: doi:10.1007/BF01231516

[Ro] M. Rosso, Finite-dimensional representations of the quantum analog of the enveloping algebra of a complex simple Lie algebra, Comm. Math. Phys. 117 (1988), no. 4, 581–593.

Mathematical Reviews (MathSciNet): MR90c:17019

Zentralblatt MATH: 0651.17008

Digital Object Identifier: doi:10.1007/BF01218386

Project Euclid: euclid.cmp/1104161818

[Sc] G. W. Schwarz, The topology of algebraic quotients, Topological methods in algebraic transformation groups (New Brunswick, NJ, 1988), Progr. Math., vol. 80, Birkhäuser Boston, Boston, MA, 1989, pp. 135–151.

Mathematical Reviews (MathSciNet): MR90m:14043

Zentralblatt MATH: 0708.14034

[Si] C. T. Simpson, Constructing variations of Hodge structure using Yang-Mills theory and applications to uniformization, J. Amer. Math. Soc. 1 (1988), no. 4, 867–918.

Mathematical Reviews (MathSciNet): MR90e:58026

Zentralblatt MATH: 0669.58008

Digital Object Identifier: doi:10.2307/1990994

JSTOR: links.jstor.org

[SL] R. Sjamaar and E. Lerman, Stratified symplectic spaces and reduction, Ann. of Math. (2) 134 (1991), no. 2, 375–422.

Mathematical Reviews (MathSciNet): MR92g:58036

Zentralblatt MATH: 0759.58019

Digital Object Identifier: doi:10.2307/2944350

JSTOR: links.jstor.org

[S1] P. Slodowy, Four lectures on simple groups and singularities, Communications of the Mathematical Institute, Rijksuniversiteit Utrecht, vol. 11, Rijksuniversiteit Utrecht Mathematical Institute, Utrecht, 1980.

Mathematical Reviews (MathSciNet): MR82b:14002

Zentralblatt MATH: 0425.22020

[S2] P. Slodowy, Simple singularities and simple algebraic groups, Lecture Notes in Mathematics, vol. 815, Springer, Berlin, 1980.

Mathematical Reviews (MathSciNet): MR82g:14037

Zentralblatt MATH: 0441.14002

previous :: next

Duke Mathematical Journal

Turn MathJax Off
What is MathJax?