Book Review
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MathSciNet review:
3077136
Full text of review:
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Book Information:
Authors:
Anders Björner and
Francesco Brenti
Title:
Combinatorics of Coxeter groups
Additional book information:
Graduate Texts in Math., vol. 231,
Springer, New York,
2005,
xiii + 363 pp.,
ISBN 3-540-44238-3,
US$74.95$
Anders Björner and Francesco Brenti, Combinatorics of Coxeter groups, Graduate Texts in Mathematics, vol. 231, Springer, New York, 2005. MR 2133266
Nicolas Bourbaki, Lie groups and Lie algebras. Chapters 4–6, Elements of Mathematics (Berlin), Springer-Verlag, Berlin, 2002. Translated from the 1968 French original by Andrew Pressley. MR 1890629, DOI 10.1007/978-3-540-89394-3
Kenneth S. Brown, Buildings, Springer-Verlag, New York, 1989. MR 969123, DOI 10.1007/978-1-4612-1019-1
H. S. M. Coxeter, Discrete groups generated by reflections, Ann. of Math. (2) 35 (1934), no. 3, 588–621. MR 1503182, DOI 10.2307/1968753
5. M.W. Davis, The Geometry and Topology of Coxeter Groups, London Math. Soc. Monographs Series, vol. 32, Princeton University Press, 2008.
James E. Humphreys, Reflection groups and Coxeter groups, Cambridge Studies in Advanced Mathematics, vol. 29, Cambridge University Press, Cambridge, 1990. MR 1066460, DOI 10.1017/CBO9780511623646
David Kazhdan and George Lusztig, Representations of Coxeter groups and Hecke algebras, Invent. Math. 53 (1979), no. 2, 165–184. MR 560412, DOI 10.1007/BF01390031
È. B. Vinberg, Hyperbolic groups of reflections, Uspekhi Mat. Nauk 40 (1985), no. 1(241), 29–66, 255 (Russian). MR 783604
- 1.
- A. Björner and F. Brenti, Combinatorics of Coxeter Groups, Graduate Texts in Math. 231, Springer, New York, 2005. MR 2133266
- 2.
- N. Bourbaki, Lie Groups and Lie Algebras, Chapters 4-6, Springer, New York, 2002. MR 1890629
- 3.
- K.S. Brown, Buildings, Springer, New York, 1989. MR 0969123
- 4.
- H.S.M. Coxeter, Discrete groups generated by reflections, Ann. of Math. 35 (1934), 588-621. MR 1503182
- 5.
- M.W. Davis, The Geometry and Topology of Coxeter Groups, London Math. Soc. Monographs Series, vol. 32, Princeton University Press, 2008.
- 6.
- J.E. Humphreys, Reflection Groups and Coxeter Groups, Cambridge University Press, Cambridge, 1990. MR 1066460
- 7.
- D. Kazhdan and G. Lusztig, Representations of Coxeter groups and Hecke algebras, Invent. Math. 53 (1979), 165-184. MR 0560412
- 8.
- E.B. Vinberg, Hyperbolic reflection groups, Russian Math. Surveys 40 (1985), 31-75. MR 0783604
Review Information:
Reviewer:
Michael W. Davis
Affiliation:
The Ohio State University
Email:
mdavis@math.ohio-state.edu
Journal:
Bull. Amer. Math. Soc.
45 (2008), 445-449
DOI:
https://doi.org/10.1090/S0273-0979-08-01170-1
Published electronically:
January 7, 2008
Review copyright:
© Copyright 2008
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.
