Book Review

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Book Information:

Author: Stephen Donkin

Title: The -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, $25.00$

**[A]**

*On the decomposition numbers of the Hecke algebra of*, J. Math. Kyoto Univ.

**36**(1996), 789-808. MR

**1443748**

**[AST]**

*Quantum deformations of*, Comm. Pure Applied Math.

**44**(1991), 879-895. MR

**1127037**

**[CP]**

*A guide to quantum groups*, Cambridge U. Press, 1994. MR

**1300632**, MR

**96h:17014**

**[CPS]**

*Generic and*

*-rational representation theory*, Publ. RIMS (Kyoto)

**35**(1999), 31-90. CMP

**99:10**

**[C]**

*Pioneers in representation theory: Frobenius, Burnside, Schur, and Brauer*, vol. 15, Amer. Math. Soc. History of Mathematics Series, 1999. CMP

**2000:02**

**[CR]**

*Methods of representation theory, Vol. II*, Wiley, 1987. MR

**0892316**

**[DD]**

*Quantum*, Proc. London Math. Soc.

**53**(1991), 165-211. MR

**1105721**

**[DJ]**

*The*

*-Schur algebra*, Proc. London Math. Soc.

**59**(1989), 23-50. MR

**0997250**

**[D]**

*Standard homological properties for quantum*, J. Algebra

**181**(1996), 400-429. MR

**1382035**

**[DPW]**

*Two-parameter quantum linear groups and the hyperbolic invariance of*

*-Schur algebras*, J. London Math. Soc.

**44**(1991), 420-436. MR

**1149005**

**[GL]**

*Cellular algebras*, Inventiones math.

**123**(1996), 1-34. MR

**1376244**

**[G]**

*Polynomial representations of*, vol. 830, Springer Lecture Notes, 1980. MR

**0606556**

**[J]**

*A*

*-analogue of*

*, Hecke algebra, and the Yang-Baxter equation*, Letters in Math. Physics

**11**(1986), 247-252. MR

**0841713**

**[KL]**

*Representations of Coxeter groups and Hecke algebras*, Inventiones math.

**53**(1979), 165-184. MR

**0560412**

**[KT]**

*Kazhdan-Lusztig conjecture for affine Lie algebras with negative level*, Duke Math. J.

**77**(1995), 21-62. MR

**1317626**

**[LLT]**

*Hecke algebras at roots of unity and crystal bases of quantum affine algebras*, Comm. Math. Physics

**181**(1996), 205-263. MR

**1410572**

**[M]**

*Quantum groups and non-commutative geometry*, Université de Montréal, 1988. MR

**1016381**

**[W]**

*The classical groups: Their invariants and representations*, Princeton U. Press, 1997. MR

**1488158**

Review Information:

Reviewer: Brian Parshall

Affiliation: University of Virginia

Email: bjp8w@virginia.edu

Journal: Bull. Amer. Math. Soc.

**37**(2000), 467-472

Published electronically: June 27, 2000

Review copyright: © Copyright 2000 American Mathematical Society