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Bulletin of the American Mathematical Society

The Bulletin publishes expository articles on contemporary mathematical research, written in a way that gives insight to mathematicians who may not be experts in the particular topic. The Bulletin also publishes reviews of selected books in mathematics and short articles in the Mathematical Perspectives section, both by invitation only.

ISSN 1088-9485 (online) ISSN 0273-0979 (print)

The 2020 MCQ for Bulletin of the American Mathematical Society is 0.84.

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Book Review

The AMS does not provide abstracts of book reviews. You may download the entire review from the links below.

Full text of review: PDF   This review is available free of charge.
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, $64.50$

References [Enhancements On Off] (What's this?)

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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
A. Beilinson, B. Feigin, B. Mazur, Introduction to algebraic field theories on curves, preprint.
A. Borel, F. Ehlers, P. Grivel, B. Kaup, A. Haefliger, B. Malgrange, Algebraic $D$-modules, Persp. in Math. 2, Acad. Press, Inc. (1987). MR 0882000
L. Crane, I. B. Frenkel. Four dimensional topological quantum field theory, Hopf categories, and the canonical bases. J. Math. Phys. 35 (1994). MR 1295461
V. Ginzburg, Perverse sheaves on a loop group and Langlands duality, preprint alg-geom/9511007.
V. Ginzburg, E. Vasserot, Langlands reciprocity for affine quantum groups of type $A\sb n$, Internat. Math. Res. Notices (1993), 67-85. MR 1208827
M. Khovanov, A categorification of the Jones polynomial, Preprint math.QA/9908171 (1999).
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
G. Lusztig, Introduction to quantum groups, Boston, Birkhäuser, 1993. MR 1227098
G. Lusztig, Intersection cohomology methods in representation theory, in Proceedings of the International Congress of Mathematicians, Kyoto, Springer-Verlag (1991). MR 1159211
I. Mirkovic, K. Vilonen, Perverse sheaves on loop Grassmannians and Langlands duality, Preprint alg-geom/9703010.
H. Nakajima, Quiver varieties and Kac-Moody algebras, Duke Math. J. 91 (1998), 515-560. MR 1604167
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Review Information:

Reviewer: Ivan Mirković
Affiliation: University of Massachusetts at Amherst
Journal: Bull. Amer. Math. Soc. 37 (2000), 343-349
Published electronically: April 3, 2000
Review copyright: © Copyright 2000 American Mathematical Society