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1567412
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Book Information:
Authors:
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.
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.
Richard Brauer, On a conjecture by Nakayama, Trans. Roy. Soc. Canada Sect. III 41 (1947), 11–19. MR 29906
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
Michael Clausen, Letter place algebras and a characteristic-free approach to the representation theory of the general linear and symmetric groups. I, Adv. in Math. 33 (1979), no. 2, 161–191. MR 544848, DOI 10.1016/S0001-8708(79)80004-3
Charles W. Curtis and Irving Reiner, Representation theory of finite groups and associative algebras, Pure and Applied Mathematics, Vol. XI, Interscience Publishers (a division of John Wiley & Sons, Inc.), New York-London, 1962. MR 0144979
J. Désarménien, Joseph P. S. Kung, and Gian-Carlo Rota, Invariant theory, Young bitableaux, and combinatorics, Advances in Math. 27 (1978), no. 1, 63–92. MR 485944, DOI 10.1016/0001-8708(78)90077-4
Larry Dornhoff, Group representation theory. Part A: Ordinary representation theory, Pure and Applied Mathematics, vol. 7, Marcel Dekker, Inc., New York, 1971. MR 0347959
Peter Doubilet, Gian-Carlo Rota, and Joel Stein, On the foundations of combinatorial theory. IX. Combinatorial methods in invariant theory, Studies in Appl. Math. 53 (1974), 185–216. MR 498650, DOI 10.1002/sapm1974533185
N. Esper, Tables of reductions of symmetrized inner products (“inner plethysms”) of ordinary irreducible representations of symmetric groups, Math. Comp. 29 (1975), no. 132, 1150–1151. MR 387398, DOI 10.1090/S0025-5718-1975-0387398-1
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.
H. K. Farahat, W. Müller, and M. H. Peel, The modular characters of the symmetric groups, J. Algebra 40 (1976), no. 2, 354–363. MR 412266, DOI 10.1016/0021-8693(76)90200-3
Roger H. Farrell, Multivariate calculation, Springer Series in Statistics, Springer-Verlag, New York, 1985. Use of the continuous groups. MR 770934, DOI 10.1007/978-1-4613-8528-8
Walter Feit, The representation theory of finite groups, North-Holland Mathematical Library, vol. 25, North-Holland Publishing Co., Amsterdam-New York, 1982. MR 661045
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, DOI 10.1112/jlms/s1-25.3.205
H. Garnir, Théorie de la représentation linéaire des groupes symétriques, Mém. Soc. Roy. Sci. Liège (4) 10 (1950), 100 (French). MR 36237
James A. Green, Polynomial representations of $\textrm {GL}_{n}$, Lecture Notes in Mathematics, vol. 830, Springer-Verlag, Berlin-New York, 1980. MR 606556
Morton Hamermesh, Group theory and its application to physical problems, Addison-Wesley Series in Physics, Addison-Wesley Publishing Co., Inc., Reading, Mass.-London, 1962. MR 0136667
19. G. Higman, Representations of general linear groups and varieties of p-groups, Proc. Internat. Conf. Theory of Groups Canberra, 1965, pp. 167-173.
Peter Hoffman, $\tau$-rings and wreath product representations, Lecture Notes in Mathematics, vol. 746, Springer, Berlin, 1979. MR 549031
I. Martin Isaacs, Character theory of finite groups, Pure and Applied Mathematics, No. 69, Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London, 1976. MR 0460423
G. D. James, The representation theory of the symmetric groups, Lecture Notes in Mathematics, vol. 682, Springer, Berlin, 1978. MR 513828
Adalbert Kerber, Representations of permutation groups. I, Lecture Notes in Mathematics, Vol. 240, Springer-Verlag, Berlin-New York, 1971. MR 0325752
Adalbert Kerber and Michael Harry Peel, On the decomposition numbers of symmetric and alternating groups, Mitt. Math. Sem. Giessen 91 (1971), 45–81. MR 296145
Donald Knutson, $\lambda$-rings and the representation theory of the symmetric group, Lecture Notes in Mathematics, Vol. 308, Springer-Verlag, Berlin-New York, 1973. MR 0364425
Walter Ledermann, Introduction to group characters, Cambridge University Press, Cambridge-New York-Melbourne, 1977. MR 0460424
27. D. E. Littlewood, Polynomial concomitants and invariant matrices, J. London Math. Soc. 11 (1936) 49-55.
D. E. Littlewood, Invariant theory, tensors and group characters, Philos. Trans. Roy. Soc. London Ser. A 239 (1944), 305–365. MR 10594, DOI 10.1098/rsta.1944.0001
Dudley E. Littlewood, The Theory of Group Characters and Matrix Representations of Groups, Oxford University Press, New York, 1940. MR 0002127
30. D. E. Littlewood and A. R. Richardson, Group characters and algebra, Philos. Trans. Roy. Soc. London A 233 (1934), 99-142.
I. G. Macdonald, Symmetric functions and Hall polynomials, Oxford Mathematical Monographs, The Clarendon Press, Oxford University Press, New York, 1979. MR 553598
James McConnell, Note on multiplication theorems for Schur functions, Combinatoire et représentation du groupe symétrique (Actes Table Ronde CNRS, Univ. Louis-Pasteur Strasbourg, Strasbourg, 1976) Lecture Notes in Math., Vol. 579, Springer, Berlin, 1977, pp. 252–257. MR 0466295
33. F. D. Murnaghan, The theory of group representations, The Johns Hopkins Press, 1938.
Tadasi Nakayama, On some modular properties of irreducible representations of symmetric groups. II, Jpn. J. Math. 17 (1941), 411–423. MR 5730, DOI 10.4099/jjm1924.17.0_{1}65
35. M. H. Peel, Modular representations of the symmetric groups, Thesis, University of Sheffield, 1969.
M. H. Peel, Hook representations of the symmetric groups, Glasgow Math. J. 12 (1971), 136–149. MR 308249, DOI 10.1017/S0017089500001245
37. M. H. Peel, Modular representations of the symmetric groups, Univ. of Calgary Research Paper No. 292, 1975.
M. H. Peel, Specht modules and symmetric groups, J. Algebra 36 (1975), no. 1, 88–97. MR 374253, DOI 10.1016/0021-8693(75)90158-1
B. M. Puttaswamaiah and John D. Dixon, Modular representations of finite groups, Pure and Applied Mathematics, No. 73, Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London, 1977. MR 0442071
G. de B. Robinson, On the Representations of the Symmetric Group, Amer. J. Math. 60 (1938), no. 3, 745–760. MR 1507943, DOI 10.2307/2371609
G. de B. Robinson, On a conjecture by Nakayama, Trans. Roy. Soc. Canada Sect. III 41 (1947), 20–25. MR 29907
G. de B. Robinson, Representation theory of the symmetric group, Mathematical Expositions, No. 12, University of Toronto Press, Toronto, 1961. MR 0125885
Daniel Edwin Rutherford, Substitutional Analysis, Edinburgh, at the University Press, 1948. MR 0027272
C. Schensted, Longest increasing and decreasing subsequences, Canadian J. Math. 13 (1961), 179–191. MR 121305, DOI 10.4153/CJM-1961-015-3
Wilhelm Specht, Die irreduziblen Darstellungen der symmetrischen Gruppe, Math. Z. 39 (1935), no. 1, 696–711 (German). MR 1545531, DOI 10.1007/BF01201387
Glânffrwd P. Thomas, On Schensted’s construction and the multiplication of Schur functions, Adv. in Math. 30 (1978), no. 1, 8–32. MR 511739, DOI 10.1016/0001-8708(78)90129-9
R. M. Thrall, On symmetrized Kronecker powers and the structure of the free Lie ring, Amer. J. Math. 64 (1942), 371–388. MR 6149, DOI 10.2307/2371691
Jacob Towber, Two new functors from modules to algebras, J. Algebra 47 (1977), no. 1, 80–104. MR 469955, DOI 10.1016/0021-8693(77)90211-3
Jacob Towber, Young symmetry, the flag manifold, and representations of $\textrm {GL}(n)$, J. Algebra 61 (1979), no. 2, 414–462. MR 559849, DOI 10.1016/0021-8693(79)90289-8
Hermann Weyl, The classical groups, Princeton Landmarks in Mathematics, Princeton University Press, Princeton, NJ, 1997. Their invariants and representations; Fifteenth printing; Princeton Paperbacks. MR 1488158
Alfred Young, The collected papers of Alfred Young (1873–1940), Mathematical Expositions, No. 21, University of Toronto Press, Toronto, Ont.-Buffalo, N.Y., 1977. With a foreword by G. de B. Robinson and a biography by H. W. Turnbull. MR 0439548
Andrey V. Zelevinsky, Representations of finite classical groups, Lecture Notes in Mathematics, vol. 869, Springer-Verlag, Berlin-New York, 1981. A Hopf algebra approach. MR 643482
A. V. Zelevinsky, A generalization of the Littlewood-Richardson rule and the Robinson-Schensted-Knuth correspondence, J. Algebra 69 (1981), no. 1, 82–94. MR 613858, DOI 10.1016/0021-8693(81)90128-9
- 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 0029906
- 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
Review Information:
Reviewer:
Jacob Towber
Journal:
Bull. Amer. Math. Soc.
8 (1983), 357-363
DOI:
https://doi.org/10.1090/S0273-0979-1983-15121-2