Remote Access Bulletin of the American Mathematical Society

Bulletin of the American Mathematical Society

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

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?)

  • [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

Review Information:

Reviewer: Ivan Mirkovic
Affiliation: University of Massachusetts at Amherst
Email: mirkovic@math.umass.edu
Journal: Bull. Amer. Math. Soc. 37 (2000), 343-349
MSC (2000): Primary 22-XX; Secondary 14-XX
DOI: https://doi.org/10.1090/S0273-0979-00-00864-8
Published electronically: April 3, 2000
Review copyright: © Copyright 2000 American Mathematical Society
American Mathematical Society