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Quivers, perverse sheaves, and quantized enveloping algebras
Author:
G. Lusztig
Journal:
J. Amer. Math. Soc. 4 (1991), 365-421
MSC:
Primary 17B37; Secondary 17B67, 20G05
MathSciNet review:
1088333
Full-text PDF Free Access
References |
Similar Articles |
Additional Information
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A.
A. Beĭlinson, J.
Bernstein, and P.
Deligne, Faisceaux pervers, Analysis and topology on singular
spaces, I (Luminy, 1981) Astérisque, vol. 100, Soc. Math.
France, Paris, 1982, pp. 5–171 (French). MR 751966
(86g:32015)
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Pierre
Deligne, La conjecture de Weil. II, Inst. Hautes Études
Sci. Publ. Math. 52 (1980), 137–252 (French). MR 601520
(83c:14017)
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Vlastimil
Dlab and Claus
Michael Ringel, Indecomposable representations of graphs and
algebras, Mem. Amer. Math. Soc. 6 (1976),
no. 173, v+57. MR 0447344
(56 #5657)
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Victor
G. Kac, Infinite-dimensional Lie algebras, Progress in
Mathematics, vol. 44, Birkhäuser Boston Inc., Boston, MA, 1983.
An introduction. MR 739850
(86h:17015)
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Masaki
Kashiwara and Pierre
Schapira, Microlocal study of sheaves, Astérisque
128 (1985), 235 (English, with French summary).
Corrections to this article can be found in Astérisque No. 130, p.
209. MR
794557 (87f:58159)
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B. Kronheimer, The construction of ALE spaces as hyper-Kähler
quotients, J. Differential Geom. 29 (1989),
no. 3, 665–683. MR 992334
(90d:53055)
- [L1]
George
Lusztig, Character sheaves. I, Adv. in Math.
56 (1985), no. 3, 193–237. MR 792706
(87b:20055), http://dx.doi.org/10.1016/0001-8708(85)90034-9
- [L2]
G.
Lusztig, Canonical bases arising from quantized
enveloping algebras, J. Amer. Math. Soc.
3 (1990), no. 2,
447–498. MR 1035415
(90m:17023), http://dx.doi.org/10.1090/S0894-0347-1990-1035415-6
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-, Canonical bases arising from quantized enveloping algebras, II, Progr. Theor. Phys. 102 (1990).
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D. MacPherson, Chern classes for singular algebraic varieties,
Ann. of Math. (2) 100 (1974), 423–432. MR 0361141
(50 #13587)
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Claus
Michael Ringel, Hall algebras and quantum groups, Invent.
Math. 101 (1990), no. 3, 583–591. MR 1062796
(91i:16024), http://dx.doi.org/10.1007/BF01231516
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A. Schofield, Notes on constructing Lie algebras from finite-dimensional algebras, preprint.
- [BBD]
- A. A. Beilinson, J. Bernstein, and P. Deligne, Faisceaux pervers, Astérisque 100 (1982). MR 751966 (86g:32015)
- [D]
- P. Deligne, La conjecture de Weil, II, Inst. Hautes Études Publ. Math. 52 (1980), 137-252. MR 601520 (83c:14017)
- [DR]
- V. Dlab and C. M. Ringel, Indecomposable representations of graphs and algebras, Mem. Amer. Math. Soc., No. 173, Amer. Math. Soc., Providence, RI, 1976. MR 0447344 (56:5657)
- [K]
- V. Kac, Infinite dimensional Lie algebras, Birkhäuser, Boston, 1983. MR 739850 (86h:17015)
- [KS]
- M. Kashiwara and P. Schapira, Microlocal study of sheaves, Astérisque 128 (1985). MR 794557 (87f:58159)
- [K]
- P. B. Kronheimer, The construction of ALE spaces as hyper-Kähler quotients, J. Differential Geom. 29 (1989), 665-683. MR 992334 (90d:53055)
- [L1]
- G. Lusztig, Character sheaves, I, Adv. in Math. 56 (1985), 193-237. MR 792706 (87b:20055)
- [L2]
- -, Canonical bases arising from quantized enveloping algebras, J. Amer. Math. Soc. 3 (1990), 447-498. MR 1035415 (90m:17023)
- [L3]
- -, Canonical bases arising from quantized enveloping algebras, II, Progr. Theor. Phys. 102 (1990).
- [M]
- R. MacPherson, Chern classes for singular varieties, Ann. of Math. (2) 100 (1974), 423-432. MR 0361141 (50:13587)
- [R]
- C. M. Ringel, Hall algebras and quantum groups, Invent. Math. (1990). MR 1062796 (91i:16024)
- [S]
- A. Schofield, Notes on constructing Lie algebras from finite-dimensional algebras, preprint.
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Additional Information
DOI:
http://dx.doi.org/10.1090/S0894-0347-1991-1088333-2
PII:
S 0894-0347(1991)1088333-2
Article copyright:
© Copyright 1991 American Mathematical Society
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