Bulletin of the American Mathematical Society

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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.

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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

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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

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D. E. Littlewood and A. R. Richardson, Group characters and algebra, Philos. Trans. Roy. Soc. London A 233 (1934), 99-142.

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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

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F. D. Murnaghan, The theory of group representations, The Johns Hopkins Press, 1938.

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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