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Book Review

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Book Information

Author(s): 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, $39.95, 0-521-64558-1

Author(s): 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, $25.00, 0-8218-1926-7

References:

[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

Additional Information:

Reviewer(s):
Brian Parshall
Affiliation: University of Virginia
Email: bjp8w@virginia.edu

Review Information:
Journal: Bull. Amer. Math. Soc. 37 (2000), 467-472.

MSC (2000): Primary 20C30, 20C33, 20G42, 17B37, 16G99; Secondary 05E10, 20G05, 20C20
DOI: 10.1090/S0273-0979-00-00874-0
PII: S 0273-0979(00)00874-0
Posted: June 27, 2000
Copyright of article: Copyright 2000, American Mathematical Society

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