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Book Review

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Book Information

Author(s): Neil Chriss and Victor Ginzburg
Title: Representation theory and complex geometry
Additional book information: Birkhäuser, Boston, 1997, x + 495, $64.50, 0-8176-3792-3

References:

[BB]
A. Beilinson, J. Bernstein, A proof of Jantzen conjectures, Adv. in Soviet Math. 16, part 1 (1993), 1-50. MR 95a:22022

[BBD]
A. Beilinson, J. Bernstein, P. Deligne, Faisceaux Pervers, Astérisque 100 (1982). MR 86g:32015

[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 97m:14008

[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 $D$-modules, Persp. in Math. 2, Acad. Press, Inc. (1987). MR 89g:32014

[CF]
L. Crane, I. B. Frenkel. Four dimensional topological quantum field theory, Hopf categories, and the canonical bases. J. Math. Phys. 35 (1994). MR 96d:57019

[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 $A\sb n$, Internat. Math. Res. Notices (1993), 67-85. MR 94j:17011

[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 87b:20055, MR 87m:20118a, MR 87m:20118b, MR 87m:20118c

[Lu2]
G. Lusztig, Introduction to quantum groups, Boston, Birkhäuser, 1993. MR 94m:17016

[Lu3]
G. Lusztig, Intersection cohomology methods in representation theory, in Proceedings of the International Congress of Mathematicians, Kyoto, Springer-Verlag (1991). MR 93e:20059

[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 99b:17033

[Ri]
C. M. Ringel, Hall algebras and quantum groups, Invent. Math. 101 (1990), 583-592. MR 91i:16024

Additional Information:

Reviewer(s):
Ivan Mirkovic
Affiliation: University of Massachusetts at Amherst
Email: mirkovic@math.umass.edu

Review Information:
Journal: Bull. Amer. Math. Soc. 37 (2000), 343-349.

MSC (2000): Primary 22-XX; Secondary 14-XX
DOI: 10.1090/S0273-0979-00-00864-8
PII: S 0273-0979(00)00864-8
Posted: April 3, 2000
Copyright of article: Copyright 2000, American Mathematical Society

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