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] S. Ariki, On the decomposition numbers of the Hecke algebra of 
, J. Math. Kyoto Univ. 36 (1996), 789-808. MR 1443748
[AST] M. Artin, W. Shelter, and J. Tate, Quantum deformations of 
, Comm. Pure Applied Math. 44 (1991), 879-895. MR 1127037
[CP] V. Chari and A. Pressley, A guide to quantum groups, Cambridge U. Press, 1994. MR 1300632, MR 96h:17014
[CPS] E. Cline, B. Parshall and L. Scott, Generic and 
-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 0892316
[DD] R. Dipper and S. Donkin, Quantum 
, Proc. London Math. Soc. 53 (1991), 165-211. MR 1105721
[DJ] R. Dipper and G. James, The 
-Schur algebra, Proc. London Math. Soc. 59 (1989), 23-50. MR 0997250
[D] S. Donkin, Standard homological properties for quantum 
, J. Algebra 181 (1996), 400-429. MR 1382035
[DPW] J. Du, B. Parshall, and J.-P. Wang, Two-parameter quantum linear groups and the hyperbolic invariance of 
-Schur algebras, J. London Math. Soc. 44 (1991), 420-436. MR 1149005
[GL] J. Graham and G. Lehrer, Cellular algebras, Inventiones math. 123 (1996), 1-34. MR 1376244
[G] J. A. Green, Polynomial representations of 
, vol. 830, Springer Lecture Notes, 1980. MR 0606556
[J] M. Jimbo, A 
-analogue of 
, Hecke algebra, and the Yang-Baxter equation, Letters in Math. Physics 11 (1986), 247-252. MR 0841713
[KL] D. Kazhdan and G. Lusztig, Representations of Coxeter groups and Hecke algebras, Inventiones math. 53 (1979), 165-184. MR 0560412
[KT] M. Kashiwara and T. Tanisaki, Kazhdan-Lusztig conjecture for affine Lie algebras with negative level, Duke Math. J. 77 (1995), 21-62. MR 1317626
[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 1410572
[M] Yu. I. Manin, Quantum groups and non-commutative geometry, Université de Montréal, 1988. MR 1016381
[W] H. Weyl, The classical groups: Their invariants and representations, Princeton U. Press, 1997. MR 1488158
- [A]
- S. Ariki, On the decomposition numbers of the Hecke algebra of , J. Math. Kyoto Univ. 36 (1996), 789-808. MR 1443748
- [AST]
- M. Artin, W. Shelter, and J. Tate, Quantum deformations of , Comm. Pure Applied Math. 44 (1991), 879-895. MR 1127037
- [CP]
- V. Chari and A. Pressley, A guide to quantum groups, Cambridge U. Press, 1994. MR 1300632, MR 96h:17014
- [CPS]
- E. Cline, B. Parshall and L. Scott, Generic and -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 0892316
- [DD]
- R. Dipper and S. Donkin, Quantum , Proc. London Math. Soc. 53 (1991), 165-211. MR 1105721
- [DJ]
- R. Dipper and G. James, The -Schur algebra, Proc. London Math. Soc. 59 (1989), 23-50. MR 0997250
- [D]
- S. Donkin, Standard homological properties for quantum , J. Algebra 181 (1996), 400-429. MR 1382035
- [DPW]
- J. Du, B. Parshall, and J.-P. Wang, Two-parameter quantum linear groups and the hyperbolic invariance of -Schur algebras, J. London Math. Soc. 44 (1991), 420-436. MR 1149005
- [GL]
- J. Graham and G. Lehrer, Cellular algebras, Inventiones math. 123 (1996), 1-34. MR 1376244
- [G]
- J. A. Green, Polynomial representations of , vol. 830, Springer Lecture Notes, 1980. MR 0606556
- [J]
- M. Jimbo, A -analogue of , Hecke algebra, and the Yang-Baxter equation, Letters in Math. Physics 11 (1986), 247-252. MR 0841713
- [KL]
- D. Kazhdan and G. Lusztig, Representations of Coxeter groups and Hecke algebras, Inventiones math. 53 (1979), 165-184. MR 0560412
- [KT]
- M. Kashiwara and T. Tanisaki, Kazhdan-Lusztig conjecture for affine Lie algebras with negative level, Duke Math. J. 77 (1995), 21-62. MR 1317626
- [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 1410572
- [M]
- Yu. I. Manin, Quantum groups and non-commutative geometry, Université de Montréal, 1988. MR 1016381
- [W]
- H. Weyl, 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
