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:

Author: Stephen Donkin
Title: The $q$-Schur algebra
Additional book information: London Mathematical Society Lecture Note Series, vol. 253, Cambridge Univ. Press, Cambridge, 1999, x + 179 pp., ISBN 0-521-64558-1, $39.95

Author: Andrew Mathas
Title: Iwahori-Hecke algebras and Schur algebras of the symmetric group
Additional book information: University Lecture Series, vol. 15, American Mathematical Society, Providence, RI, 1999, xiii + 188 pp., ISBN 0-8218-1926-7, $25.00

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

  • [A] S. Ariki, On the decomposition numbers of the Hecke algebra of $G(m,1,n)$, J. Math. Kyoto Univ. 36 (1996), 789-808. MR 98h:20012
  • [AST] M. Artin, W. Shelter, and J. Tate, Quantum deformations of $GL_m$, Comm. Pure Applied Math. 44 (1991), 879-895. MR 92i:17014
  • [CP] V. Chari and A. Pressley, A guide to quantum groups, Cambridge U. Press, 1994. MR 95j:17010, MR 96h:17014
  • [CPS] E. Cline, B. Parshall and L. Scott, Generic and $q$-rational representation theory, Publ. RIMS (Kyoto) 35 (1999), 31-90. CMP 99:10
  • [C] C. W. Curtis, Pioneers in representation theory: Frobenius, Burnside, Schur, and Brauer, vol. 15, Amer. Math. Soc. History of Mathematics Series, 1999. CMP 2000:02
  • [CR] C. W. Curtis and I. Reiner, Methods of representation theory, Vol. II, Wiley, 1987. MR 88f:20002
  • [DD] R. Dipper and S. Donkin, Quantum $GL_n$, Proc. London Math. Soc. 53 (1991), 165-211. MR 92g:16055
  • [DJ] R. Dipper and G. James, The $q$-Schur algebra, Proc. London Math. Soc. 59 (1989), 23-50. MR 90g:16026
  • [D] S. Donkin, Standard homological properties for quantum $GL_n$, J. Algebra 181 (1996), 400-429. MR 97b:20065
  • [DPW] J. Du, B. Parshall, and J.-P. Wang, Two-parameter quantum linear groups and the hyperbolic invariance of $q$-Schur algebras, J. London Math. Soc. 44 (1991), 420-436. MR 93d:20084
  • [GL] J. Graham and G. Lehrer, Cellular algebras, Inventiones math. 123 (1996), 1-34. MR 97h:20016
  • [G] J. A. Green, Polynomial representations of $GL_n$, vol. 830, Springer Lecture Notes, 1980. MR 83j:20003
  • [J] M. Jimbo, A $q$-analogue of $U(\mathfrak{gl}(N+1))$, Hecke algebra, and the Yang-Baxter equation, Letters in Math. Physics 11 (1986), 247-252. MR 87k:17011
  • [KL] D. Kazhdan and G. Lusztig, Representations of Coxeter groups and Hecke algebras, Inventiones math. 53 (1979), 165-184. MR 81j:20066
  • [KT] M. Kashiwara and T. Tanisaki, Kazhdan-Lusztig conjecture for affine Lie algebras with negative level, Duke Math. J. 77 (1995), 21-62. MR 96j:17016
  • [LLT] A. Lascoux, B. Leclerc, and Y.-Y. Thibon, Hecke algebras at roots of unity and crystal bases of quantum affine algebras, Comm. Math. Physics 181 (1996), 205-263. MR 97k:17019
  • [M] Yu. I. Manin, Quantum groups and non-commutative geometry, Université de Montréal, 1988. MR 91e:17001
  • [W] H. Weyl, The classical groups: Their invariants and representations, Princeton U. Press, 1997. MR 98k:01049

Review Information:

Reviewer: Brian Parshall
Affiliation: University of Virginia
Email: bjp8w@virginia.edu
Journal: Bull. Amer. Math. Soc. 37 (2000), 467-472
MSC (2000): Primary 20C30, 20C33, 20G42, 17B37, 16G99; Secondary 05E10, 20G05, 20C20
Published electronically: June 27, 2000
Review copyright: © Copyright 2000 American Mathematical Society
American Mathematical Society