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Bulletin of the American Mathematical Society

The Bulletin publishes expository articles on contemporary mathematical research, written in a way that gives insight to mathematicians who may not be experts in the particular topic. The Bulletin also publishes reviews of selected books in mathematics and short articles in the Mathematical Perspectives section, both by invitation only.

ISSN 1088-9485 (online) ISSN 0273-0979 (print)

The 2020 MCQ for Bulletin of the American Mathematical Society is 0.84.

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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: Stuart Martin
Title: Schur algebras and representation theory
Additional book information: Cambridge Tracts in Math., vol. 112, Cambridge University Press, Cambridge, 1993, xv + 232 pp., ISBN 0-521-41591-8, $44.95$

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

  • Michael Artin, William Schelter, and John Tate, Quantum deformations of $\textrm {GL}_n$, Comm. Pure Appl. Math. 44 (1991), no. 8-9, 879–895. MR 1127037, DOI 10.1002/cpa.3160440804
  • Roger W. Carter and George Lusztig, On the modular representations of the general linear and symmetric groups, Math. Z. 136 (1974), 193–242. MR 354887, DOI 10.1007/BF01214125
  • E. Cline, B. Parshall, and L. Scott, Finite-dimensional algebras and highest weight categories, J. Reine Angew. Math. 391 (1988), 85–99. MR 961165
  • Richard Dipper, Polynomial representations of finite general linear groups in nondescribing characteristic, Representation theory of finite groups and finite-dimensional algebras (Bielefeld, 1991) Progr. Math., vol. 95, Birkhäuser, Basel, 1991, pp. 343–370. MR 1112168
  • Richard Dipper and Stephen Donkin, Quantum $\textrm {GL}_n$, Proc. London Math. Soc. (3) 63 (1991), no. 1, 165–211. MR 1105721, DOI 10.1112/plms/s3-63.1.165
  • Richard Dipper and Gordon James, The $q$-Schur algebra, Proc. London Math. Soc. (3) 59 (1989), no. 1, 23–50. MR 997250, DOI 10.1112/plms/s3-59.1.23
  • [Do1]
    S. Donkin, The blocks of a semisimple group, J. Algebra 67 (1980), 36--53.
  • S. Donkin, On Schur algebras and related algebras. I, J. Algebra 104 (1986), no. 2, 310–328. MR 866778, DOI 10.1016/0021-8693(86)90218-8
  • Stephen Donkin, On Schur algebras and related algebras. IV. The blocks of the Schur algebras, J. Algebra 168 (1994), no. 2, 400–429. MR 1292772, DOI 10.1006/jabr.1994.1236
  • Jie Du, Brian Parshall, and Jian Pan Wang, Two-parameter quantum linear groups and the hyperbolic invariance of $q$-Schur algebras, J. London Math. Soc. (2) 44 (1991), no. 3, 420–436. MR 1149005, DOI 10.1112/jlms/s2-44.3.420
  • Ferdinand Georg Frobenius, Gesammelte Abhandlungen. Bände I, II, III, Springer-Verlag, Berlin-New York, 1968 (German). Herausgegeben von J.-P. Serre. MR 0235974
  • James A. Green, Polynomial representations of $\textrm {GL}_{n}$, Lecture Notes in Mathematics, vol. 830, Springer-Verlag, Berlin-New York, 1980. MR 606556
  • G. D. James, The representation theory of the symmetric groups, Lecture Notes in Mathematics, vol. 682, Springer, Berlin, 1978. MR 513828
  • Michio Jimbo, A $q$-analogue of $U({\mathfrak {g}}{\mathfrak {l}}(N+1))$, Hecke algebra, and the Yang-Baxter equation, Lett. Math. Phys. 11 (1986), no. 3, 247–252. MR 841713, DOI 10.1007/BF00400222
  • I. G. Macdonald, Symmetric functions and Hall polynomials, Oxford Mathematical Monographs, The Clarendon Press, Oxford University Press, New York, 1979. MR 553598
  • Brian J. Parshall, Finite-dimensional algebras and algebraic groups, Classical groups and related topics (Beijing, 1987) Contemp. Math., vol. 82, Amer. Math. Soc., Providence, RI, 1989, pp. 97–114. MR 982281, DOI 10.1090/conm/082/982281
  • [PS1]
    B. Parshall and L. Scott, Derived categories, quasi-hereditary algebras, and algebraic groups, Carlton Univ. Math. Notes 3 (1989), 1--105.
  • T. Venkatarayudu, The $7$-$15$ problem, Proc. Indian Acad. Sci., Sect. A. 9 (1939), 531. MR 0000001, DOI 10.1090/gsm/058
  • Brian Parshall and Jian Pan Wang, Quantum linear groups, Mem. Amer. Math. Soc. 89 (1991), no. 439, vi+157. MR 1048073, DOI 10.1090/memo/0439
  • Issai Schur, Gesammelte Abhandlungen. Band I, Springer-Verlag, Berlin-New York, 1973 (German). Herausgegeben von Alfred Brauer und Hans Rohrbach. MR 0462891
  • Issai Schur, Gesammelte Abhandlungen. Band I, Springer-Verlag, Berlin-New York, 1973 (German). Herausgegeben von Alfred Brauer und Hans Rohrbach. MR 0462891
  • Leonard L. Scott, Simulating algebraic geometry with algebra. I. The algebraic theory of derived categories, The Arcata Conference on Representations of Finite Groups (Arcata, Calif., 1986) Proc. Sympos. Pure Math., vol. 47, Amer. Math. Soc., Providence, RI, 1987, pp. 271–281. MR 933417
  • Robert Steinberg, Representations of algebraic groups, Nagoya Math. J. 22 (1963), 33–56. MR 155937
  • [W]
    H. Weyl, The classical groups, Princeton: Princeton U. Press, 1939.

    Review Information:

    Reviewer: Brian Parshall
    Affiliation: University of Virginia
    Journal: Bull. Amer. Math. Soc. 33 (1996), 371-375
    Review copyright: © Copyright 1996 American Mathematical Society