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Book Review
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Book Information
Author(s):
Gordon James and Adalbert Kerber
Title:
The representation theory of the symmetric group
Additional book information:
Encyclopedia of Mathematics and its Applications, vol. 16, Addison-Wesley, Reading, Mass., 1981, xxviii + 510 pp., $44.50
References:
- 1.
- K. Baclawski, Combinatorial algorithms for Young tableaux, Lecture Notes, Univ. of California, San Diego, 1980.
- 2.
- H. Boerner, Representations of groups, 2nd ed., North-Holland, Amsterdam, 1967, 1970.
- 3.
- R. Brauer, On a conjecture by Nakayama, Trans. Roy. Soc. Canada Sect. III (3) 41 (1947), 11-19. MR 29906
- 4.
- R. W. Carter and G. Lusztig, On the modular representations of the general linear and symmetric groups, Math. Z. 136 (1974), 193-242. MR 354887
- 5.
- M. Clausen, Letter place algebras and a characteristic-free approach to the representation theory of the general linear and symmetric groups. I, II, Adv. in Math. 33 (1979), 161-191; 38 (1980), 152-177. MR 544848
- 6.
- C. W. Curtis and I. Reiner, Representation theory of finite groups and associative algebras, vol. 11, Wiley, New York, London, Sydney, 1962. MR 144979
- 7.
- J. Désarménian, J. P. S. Kung and G. -C. Rota, Invariant theory, Young bitableaux and combinatorics, Adv. in Math. 27 (1978), 63-92. MR 485944
- 8.
- L. Dornhoff, Group representation theory, Part B, Dekker, New York, 1972. MR 347960
- 9.
- P. Doubilet, G.-C. Rota and J. Stein, On the foundation of combinatorial theory IX: Combinatorial methods in invariant theory, Stud. Appl. Math. 79 (1973), 177-179. MR 498650
- 10.
- N. Esper, Tables of reduction of symmetrized inner products ('inner plethysms') of ordinary irreducible representations of symmetric groups, Math. Comp. 29 (1975), 1150-1151. MR 387398
- 11.
- H. K. Farahat, A. Kerber and M. H. Peel, Modular representation theory of the symmetric groups, Research paper no. 131, The University of Calgary, 1971.
- 12.
- H. K. Farahat, W. Müller and M. H. Peel, The modular characters of the symmetric groups, J. Alg. 40 (1976), 354-363. MR 412266
- 13.
- R. H. Farrell, Techniques of multivariate calculation, Lecture Notes in Math., vol. 520, Springer-Verlag, Berlin and New York, 1976. MR 770934
- 14.
- W. Feit, The representation theory of finite groups, North-Holland, New York, 1981. MR 661045
- 15.
- H. O. Foulkes, Concomitants of the quintic and sextic up to degree four in the coefficients of the ground form, J. London Math. Soc. 25 (1950), 205-209. MR 37276
- 16.
- H. Garnir, Théorie de la représentation lineaire des groupes symétriques, Mem. Soc. Roy. Sci. Liege (4) 10 (1950), no. 2, 5-100. MR 36237
- 17.
- J. A. Green, Polynomial representations of GL, Lecture Notes in Math., vol. 830, Springer-Verlag, Berlin and New York, 1980. MR 606556
- 18.
- M. Hamermesh, Group theory and its applications to physical problems, Addison-Wesley, Reading, Mass., 1962. MR 136667
- 19.
- G. Higman, Representations of general linear groups and varieties of p-groups, Proc. Internat. Conf. Theory of Groups Canberra, 1965, pp. 167-173.
- 20.
- P. Hoffman, λ-rings and wreath product representations, Lecture Notes in Math., vol. 746, Springer-Verlag, Berlin and New York, 1979. MR 549031
- 21.
- I. M. Isaacs, Character theory of finite groups, Academic Press, New York, San Francisco, London, 1976. MR 460423
- 22.
- G. D. James, The representation theory of the symmetric groups, Lecture Notes in Math., vol. 682, Springer-Verlag, Berlin and New York, 1978. MR 513828
- 23.
- A. Kerber, Representations of permutation groups. I, II, Lecture Notes in Math., vols. 240, 495, Springer-Verlag, Berlin and New York, 1971, 1975. MR 325752
- 24.
- A. Kerber and M. H. Peel, On the decomposition numbers of symmetric and alternating groups, Mitt. Math. Sem. Univ. Giessen 91 (1971), 45-81. MR 296145
- 25.
- D. Knutson, λ-rings and the representation theory of the symmetric group, Lecture Notes in Math., vol. 308, Springer-Verlag, Berlin and New York, 1973. MR 364425
- 26.
- W. Ledermann, Introduction to group characters, Cambridge Univ. Press, London, New York, 1977. MR 460424
- 27.
- D. E. Littlewood, Polynomial concomitants and invariant matrices, J. London Math. Soc. 11 (1936) 49-55.
- 28.
- D. E. Littlewood, Invariant theory, tensors and group characters, Philos. Trans. Roy. Soc. (A) 239 (1944), 305-365. MR 10594
- 29.
- D. E. Littlewood, The theory of groups, characters and matrix representations of groups, 2nd ed., Clarendon Press, Oxford, 1950. MR 2127
- 30.
- D. E. Littlewood and A. R. Richardson, Group characters and algebra, Philos. Trans. Roy. Soc. London A 233 (1934), 99-142.
- 31.
- I. G. Macdonald, Symmetric functions and Hall polynomials, Oxford Univ. Press, London and New York, 1979. MR 553598
- 32.
- J. McConnell, Note on multiplication theorems for Schur functions, Combinatoire et réprésentation du Group Symétrique (Actes Table Ronde C. N. R. S., Univ. Louis-Pasteur, Strasbourg, 1976), Lecture Notes in Math., vol. 579, Springer-Verlag, Berlin and New York, 1977, pp. 252-257. MR 466295
- 33.
- F. D. Murnaghan, The theory of group representations, The Johns Hopkins Press, 1938.
- 34.
- T. Nakayama, On some modular properties of irreducible representations of a symmetric group. II, Japan J. Math. 17 (1940), 411-423. MR 5730
- 35.
- M. H. Peel, Modular representations of the symmetric groups, Thesis, University of Sheffield, 1969.
- 36.
- M. H. Peel, Hook representations of the symmetric groups, Glasgow Math. J. 12(1971), 136-149. MR 308249
- 37.
- M. H. Peel, Modular representations of the symmetric groups, Univ. of Calgary Research Paper No. 292, 1975.
- 38.
- M. H. Peel, Specht modules and the symmetric groups, J. Algebra 36 (1975), 88-97. MR 374253
- 39.
- B. M. Puttaswamaiah and J. D. Dixon, Modular representations of finite groups, Academic Press, New York, San Francisco, London, 1977. MR 442071
- 40.
- G. de B. Robinson, On the representations of the symmetric group. Amer. J. Math. 60 (1938), 745-7860. MR 1507943
- 41.
- G. de B. Robinson, On a conjecture by Nakayama, Trans. Roy. Soc., Canada Sect. III (3) 41 (1947), 20-25. MR 29907
- 42.
- G. de B. Robinson, Representation theory of the symmetric group, Mathematical Expositions No. 12, Univ. of Toronto Press, Toronto, 1961. MR 125885
- 43.
- D. E. Rutherford, Substitutional analysis, University Press, Edinburgh, 1948. MR 27272
- 44.
- G. Schensted, Longest increasing and decreasing subsequences, Canad. J. Math. 13 (1961). MR 121305
- 45.
- W. Specht, Die irreduziblen Darstellungen der symmetrischen Gruppe, Math. Z. 39 (1935), 696-711. MR 1545531
- 46.
- G. P. Thomas, On Schensted 's construction and the multiplication of Schur-functions, Adv. in Math. 30 (1978), 8-32. MR 511739
- 47.
- R. M. Thrall, On symmetrized Kronecker powers and the structure of the free Lie ring, Amer. J. Math. 64 (1942), 371-388. MR 6149
- 48.
- J. Towber, Two new functors from modules to algebras, J. Algebra 47 (1977), 80-104. MR 469955
- 49.
- J. Towber, Young symmetry, the flag manifold, and representations of GL(n), J. Algebra 61 (1979), 414-462. MR 559849
- 50.
- H. Weyl, The classical groups, their invariants and representations, Princeton Univ. Press, Princeton, N. J., 1939. MR 1488158
- 51.
- A. Young, Collected papers, Mathematical Expositions No. 21, Univ. of Toronto Press, Toronto, 1977. MR 439548
- 52.
- A. V. Zelevinsky, Representations of finite classical groups: A Hopf algebra approach, Lecture Notes in Math., vol. 869, Springer-Verlag, Berlin and New York, 1981. MR 643482
- 53.
- A. V. Zelevinsky, A generalization of the Littlewood-Richardson rule and the Robinson-Schenutel-Knuth correspondence, J. Algebra 69 (1981), 82-94. MR 613858
Additional Information:
Reviewer(s):
Jacob
Towber
Review Information:
Journal:
Bull. Amer. Math. Soc.
8
(1983),
357-363.
DOI:
10.1090/S0273-0979-1983-15121-2
PII:
S 0273-0979(1983)15121-2
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