Book Review
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Book Information:
Authors:
Neil Chriss and
Victor Ginzburg
Title:
Representation theory and complex geometry
Additional book information:
Birkhäuser,
Boston,
1997,
x + 495 pp.,
ISBN 0-8176-3792-3,
$64.50$
[BB] A. Beilinson, J. Bernstein, A proof of Jantzen conjectures, Adv. in Soviet Math. 16, part 1 (1993), 1-50. MR 1237825
[BBD] A. Beilinson, J. Bernstein, P. Deligne, Faisceaux Pervers, Astérisque 100 (1982). MR 0751966
[BD] A. A. Beilinson, V. G. Drinfeld, Quantization of Hitchin's fibration and Langlands' program. Math. Phys. Stud. 19, Kluwer Acad. Publ. (1996), 3-7. Chiral algebras. MR 1385674
[BFM] A. Beilinson, B. Feigin, B. Mazur, Introduction to algebraic field theories on curves, preprint.
[BEGKHM] A. Borel, F. Ehlers, P. Grivel, B. Kaup, A. Haefliger, B. Malgrange, Algebraic 
-modules, Persp. in Math. 2, Acad. Press, Inc. (1987). MR 0882000
[CF] L. Crane, I. B. Frenkel. Four dimensional topological quantum field theory, Hopf categories, and the canonical bases. J. Math. Phys. 35 (1994). MR 1295461
[Gi] V. Ginzburg, Perverse sheaves on a loop group and Langlands duality, preprint alg-geom/9511007.
[GV] V. Ginzburg, E. Vasserot, Langlands reciprocity for affine quantum groups of type 
, Internat. Math. Res. Notices (1993), 67-85. MR 1208827
[Kh] M. Khovanov, A categorification of the Jones polynomial, Preprint math.QA/9908171 (1999).
[Lu1] G. Lusztig, Character sheaves I, II, III, IV, V, Adv. Math. 56 (1985), 193-237, 57 (1985), 226-265 and 266-315, 59 (1986), 1-63, 61 (1986), 103-155. MR 0792706, MR 87m:20118a, MR 87m:20118b, MR 87m:20118c
[Lu2] G. Lusztig, Introduction to quantum groups, Boston, Birkhäuser, 1993. MR 1227098
[Lu3] G. Lusztig, Intersection cohomology methods in representation theory, in Proceedings of the International Congress of Mathematicians, Kyoto, Springer-Verlag (1991). MR 1159211
[MV] I. Mirkovic, K. Vilonen, Perverse sheaves on loop Grassmannians and Langlands duality, Preprint alg-geom/9703010.
[Na] H. Nakajima, Quiver varieties and Kac-Moody algebras, Duke Math. J. 91 (1998), 515-560. MR 1604167
[Ri] C. M. Ringel, Hall algebras and quantum groups, Invent. Math. 101 (1990), 583-592. MR 1062796
- [BB]
- A. Beilinson, J. Bernstein, A proof of Jantzen conjectures, Adv. in Soviet Math. 16, part 1 (1993), 1-50. MR 1237825
- [BBD]
- A. Beilinson, J. Bernstein, P. Deligne, Faisceaux Pervers, Astérisque 100 (1982). MR 0751966
- [BD]
- A. A. Beilinson, V. G. Drinfeld, Quantization of Hitchin's fibration and Langlands' program. Math. Phys. Stud. 19, Kluwer Acad. Publ. (1996), 3-7. Chiral algebras. MR 1385674
- [BFM]
- A. Beilinson, B. Feigin, B. Mazur, Introduction to algebraic field theories on curves, preprint.
- [BEGKHM]
- A. Borel, F. Ehlers, P. Grivel, B. Kaup, A. Haefliger, B. Malgrange, Algebraic -modules, Persp. in Math. 2, Acad. Press, Inc. (1987). MR 0882000
- [CF]
- L. Crane, I. B. Frenkel. Four dimensional topological quantum field theory, Hopf categories, and the canonical bases. J. Math. Phys. 35 (1994). MR 1295461
- [Gi]
- V. Ginzburg, Perverse sheaves on a loop group and Langlands duality, preprint alg-geom/9511007.
- [GV]
- V. Ginzburg, E. Vasserot, Langlands reciprocity for affine quantum groups of type , Internat. Math. Res. Notices (1993), 67-85. MR 1208827
- [Kh]
- M. Khovanov, A categorification of the Jones polynomial, Preprint math.QA/9908171 (1999).
- [Lu1]
- G. Lusztig, Character sheaves I, II, III, IV, V, Adv. Math. 56 (1985), 193-237, 57 (1985), 226-265 and 266-315, 59 (1986), 1-63, 61 (1986), 103-155. MR 0792706, MR 87m:20118a, MR 87m:20118b, MR 87m:20118c
- [Lu2]
- G. Lusztig, Introduction to quantum groups, Boston, Birkhäuser, 1993. MR 1227098
- [Lu3]
- G. Lusztig, Intersection cohomology methods in representation theory, in Proceedings of the International Congress of Mathematicians, Kyoto, Springer-Verlag (1991). MR 1159211
- [MV]
- I. Mirkovic, K. Vilonen, Perverse sheaves on loop Grassmannians and Langlands duality, Preprint alg-geom/9703010.
- [Na]
- H. Nakajima, Quiver varieties and Kac-Moody algebras, Duke Math. J. 91 (1998), 515-560. MR 1604167
- [Ri]
- C. M. Ringel, Hall algebras and quantum groups, Invent. Math. 101 (1990), 583-592. MR 1062796
Review Information:
Reviewer:
Ivan Mirković
Affiliation:
University of Massachusetts at Amherst
Email:
mirkovic@math.umass.edu
Journal:
Bull. Amer. Math. Soc.
37 (2000), 343-349
DOI:
https://doi.org/10.1090/S0273-0979-00-00864-8
Published electronically:
April 3, 2000
Review copyright:
© Copyright 2000
American Mathematical Society
