Remote Access Bulletin of the American Mathematical Society

Bulletin of the American Mathematical Society

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

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: G. de B. Robinson
Title: The collected papers of Alfred Young
Additional book information: University of Toronto Press, Toronto and Buffalo, 1977, xxvii + 684 pp., $10.00.

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

  • 1. G. E. Baird and L. C. Biedenharn, On the representations of semisimple Lie groups. II, J. Mathematical Phys. 4 (1963), 1449-1466. MR 156922
  • 2. D. E. Barton and F. N. David, Combinatorial chance, Griffin, London, 1962. MR 155371
  • 3. D. E. Barton and C. L. Mallows, Some aspects of the random sequence, Ann. Math. Statist. 36 (1965), 236-260. MR 178488
  • 4. Johan G. F. Belinfante and Bernard Kolman, A survey of Lie groups and Lie algebras with applications and computational methods, Classics in Applied Mathematics, vol. 2, Society for Industrial and Applied Mathematics (SIAM), Philadelphia, PA, 1989. Reprint of the 1972 original. MR 1015710
  • 5. M. Benard, On the Schur indices of characters of the exceptional Weyl groups, Ann. of Math. (2) 94 (1971), 89-107. MR 297887
  • 6. M. Benard, Schur indices and splitting fields of the unitary reflection groups, J. Algebra 38 (1976), 318-342. MR 401901
  • 7. C. T. Benson and L. C. Grove, The Schur indices of the reflection group F4, J. Algebra 27 (1973), 574-578. MR 327881
  • 8. C. Berge, Principes de combinatoire, Dunod, Paris, 1968. MR 237346
  • 9. L. C. Biedenharn and J. D. Louck, Angular momentum in quantum physics, Encyclopedia of Mathematics and its Applications, vol. 8, Addison-Wesley Publishing Co., Reading, Mass., 1981. Theory and application; With a foreword by Peter A. Carruthers. MR 635121
  • 10. W. H. Burge, Four correspondences between graphs and generalized Young tableaux, J. Combinatorial Theory (A) 17 (1974), 12-30. MR 351884
  • 11. H.-T. Chen, Collective motions of the isospin degrees of freedom of a system of paired nucleons, Nuclear Phys. A 212 (1973), 317-340.
  • 12. F. R. K. Chung and J. E. Herman, Some results on hook lengths, Discrete Math. 20 (1977), 33-40. MR 463279
  • 13. J. A. Dieudonné and J. B. Carrell, Invariant theory old and new, Academic Press, New York, 1971. MR 279102
  • 14. R. Elazer, On a problem of random walk in space, Canad. Math. Bull. 14 (1971), 503-506. MR 368098
  • 15. P. Erdös and G. Szekeres, A combinatorial problem in geometry, Compositio Math. 2 (1935), 463–470. MR 1556929
  • 16. M. B. Faist, Angular entropy: the information content of molecular scattering angular distributions, J. Chem. Phys. 66 (1977), 511-523.
  • 17. C. S. Fisher, The death of a mathematical theory: a study in the sociology of knowledge, Arch. History Exact Sci. 3 (1966), 137-159. MR 202546
  • 18. D. Foata, Une propriété du vidage-remplissage des tableaux de Young, from Combinatoire et Représentation d Groupe Symétrique, Lecture Notes in Math., vol. 579, Springer-Verlag, Berlin and New York, 1977, pp. 121-135. MR 466293
  • 19. D. Foata, (editor), Combinatoire et représentation du groupe symétrique, Lecture Notes in Math., vol. 579, Springer-Verlag, Berlin and New York, 1977. MR 466293
  • 20. H. O. Foulkes, Paths in ordered structures of partitions, Discrete Math. 9 (1974), 365-374. MR 387071
  • 21. H. O. Foulkes, Eulerian numbers, Newcomb's problem and representations of symmetric groups (to appear). MR 20080
  • 22. H. O. Foulkes, Recurrences for characters of the symmetric group, Discrete Math. 21 (1978), no. 2, 137–144. MR 523061, https://doi.org/10.1016/0012-365X(78)90086-9
  • 23. J. S. Frame, G. deB. Robinson and R. M. Thrall, The hook graph of the symmetric groups, Canad. J. Math. 6 (1954), 316-323. MR 62127
  • 24. G. Frobenius, Über die charakteristischen Einheiten der symmätrischen Gruppe, Berliner Sitzungsberichte (1903), 328-358 (also, Gesammelte Abhandlungen, vol. 3, Springer-Verlag, Berlin, 1968, pp. 244-274).
  • 25. G. Frobenius, Gesammelte Abhandlungen, 3 vols., Springer-Verlag Berlin and New York, 1968.
  • 26. A. M. Garsia and J. Remmel, On the raising operators of Alfred Young, Relations between combinatorics and other parts of mathematics (Proc. Sympos. Pure Math., Ohio State Univ., Columbus, Ohio, 1978) Proc. Sympos. Pure Math., XXXIV, Amer. Math. Soc., Providence, R.I., 1979, pp. 181–198. MR 525327
  • 27. A. M. Garsia and J. Remmel, Symmetric functions and raising operators, Linear and Multilinear Algebra 10 (1981), no. 1, 15–23. MR 615022, https://doi.org/10.1080/03081088108817389
  • 28. J. H. Grace and A. Young, The algebra of invariants, Cambridge Univ. Press, London, 1903 (reprinted: Chelsea, New York).
  • 29. C. Greene, An extension of Schensted's theorem, Advances in Math. 14 (1974), 254-265. MR 354395
  • 30. C. Greene, Some partitions associated with a partially ordered set, J. Combinatorial Theory 20 (1976), 69-79. MR 398912
  • 31. C. Greene, Some order-theoretic properties of the Robinson-Schensted correspondence, Combinatoire et Représentation du Groupe Symétrique, Lecture Notes in Math., vol. 579, Springer-Verlag, Berlin and New York, 1977, pp. 114-120. MR 462965
  • 32. L. C. Grove, The characters of the hecatonicosahedroidal group, J. Reine Angew. Math. 265 (1974), 160-169. MR 330275
  • 33. Thomas Hawkins, Hypercomplex numbers, lie groups, and the creation of group representation theory, Arch. History Exact Sci. 8 (1972), no. 4, 243–287. MR 1554156, https://doi.org/10.1007/BF00328434
  • 34. P. Hoefsmit, Representations of generic algebras corresponding to classical Weyl groups, Notices Amer. Math. Soc. 23 (1976), A297-A298.
  • 35. David Hilbert, Ueber die Theorie der algebraischen Formen, Math. Ann. 36 (1890), no. 4, 473–534 (German). MR 1510634, https://doi.org/10.1007/BF01208503
  • 36. A. P. Hillman and R. M. Grassl, Reverse plane partitions and tableau hook numbers, J. Combinatorial Theory 21 (1976), 216-221. MR 414387
  • 37. A. P. Hillman and R. M. Grassl, Tableaux enumeration and Wronskians, Notices Amer. Math. Soc. 23 (1976), A674.
  • 38. A. P. Hillman and R. M. Grassl, Functions on tableau frames, Notices Amer. Math. Soc. 24 (1977), A636.
  • 39. A. P. Hillman and R. M. Grassl, Polynomial ring generated by tableau shapes, European J. Combin. 2 (1981), no. 1, 27–39. MR 611929, https://doi.org/10.1016/S0195-6698(81)80018-2
  • 40. D. B. Hunter, On a result of Young's quantitative substitutional analysis, Proc. Edinburgh Math. Soc. 15 (1967), 257-262. MR 228599
  • 41. D. B. Hunter, The reduction of a direct product of compound matrices, Quart. J. Math. Oxford Ser. 18 (1967), 199-206. MR 219558
  • 42. D. B. Hunter, The reduction of a direct product of induced matrices, Quart. J. Math. Oxford Ser. 19 (1968), 81-87. MR 222098
  • 43. D. B. Hunter, Unitary representations of the unitary group, Proc. Cambridge Philos. Soc. 65 (1969), 377-386. MR 236281
  • 44. G. D. James, Representations of the symmetric groups over the field of order 2, J. Algebra 38 (1976), 280-308. MR 396734
  • 45. G. D. James, irreducible representations of the symmetric groups, Bull. London Math. Soc. 8 (1976), 229-232. MR 417272
  • 46. G. D. James, On the decomposition matrices of the symmetric groups. I, J. Algebra 43 (1976), 42-44. MR 430049
  • 47. G. D. James, On the decomposition matrices of the symmetric groups. II, J. Algebra 43 (1976), 45-54. MR 430050
  • 48. G. D. James, A characteristic-free approach to the representation theory of S, J. Algebra 46 (1977), 430-450. MR 439924
  • 49. G. D. James, Some combinatorial results involving Young diagrams, Proc. Cambridge Philos. Soc. 83 (1978), 1-10. MR 463280
  • 50. G. D. James, On a conjecture of Carter concerning irreducible Specht modules, Proc. Cambridge Philos. Soc. 83 (1978), 11-17. MR 463281
  • 51. G. D. James, The representation theory of the symmetric groups, Lecture Notes in Mathematics, vol. 682, Springer, Berlin, 1978. MR 513828
  • 52. A. Kerber, On a connection between the representation theories of symmetric groups and general finite groups, Proceedings of the Alfred Young Day Conference, Waterloo, 1978.
  • 53. D. Knuth, Permutations, matrices and generalized Young tableaux, Pacific J. Math. 34 (1970), 709-727. MR 272654
  • 54. 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
  • 55. G. Kreweras, Sur une classe de problèmes de dénombrement liés au treillis des partitions des entiers, Cahiers du B. U. R. O., No. 6, Paris, 1965.
  • 56. G. Kreweras, Sur une extension du problème dit "Simon Newcomb", C. R. Acad. Sci. Paris Sér. A, 263 (1966), 43-45. MR 200180
  • 57. G. Kreweras, Traitement simultané du "problème de Young" et du "problème de Simon Newcomb", Cahiers du B. U. R. O., No. 10, Paris, 1967.
  • 58. G. Kreweras, Inversion des polynômes de Bell bidimensionnels et application au dénombrement des relations binaires connexes, C. R. Acad. Sci. Paris Sér. A 268 (1969), 577-579. MR 252239
  • 59. G. Kreweras, Dénombrement systématiques de relations binaires externes, Math. et Sciences Humaines, 7 année, No. 26, 1969, pp. 5-15. MR 265183
  • 60. G. Kreweras, Sur les éventails de segments, Cahiers du B. U. R. O., No. 15, Paris, 1970.
  • 61. G. Kreweras, Standard Young tableaux and families of segments, Proceedings of the Alfred Young Day Conference, Waterloo, June 2, 1978, T. V. Narayana (editor).
  • 62. B. Lesche, A theorem on Ruch's principle of nonequilibrium statistics, J. Mathematical Phys. 17 (1976), 427-430. MR 403520
  • 63. B. Lesche and E. Ruch, Information extent and information distance, J. Chem. Phys. 69 (1978), 393-401.
  • 64. D. E. Littlewood, The theory of group characters, 2nd ed., Oxford Univ. Press, London, 1950.
  • 65. D. E. Littlewood, A University algebra, 2nd ed., Heinemann Educational Books, London (reprinted: Dover, New York, 1970). MR 345745
  • 66. D. E. Littlewood, The skeleton key of mathematics, Hutchinson Univ. Library, London, 1960 (Reprinted in French translation: Le passe-partout mathématique, Masson et Cie, Paris, 1964).
  • 67. I. G. Macdonald, On the degrees of the irreducible representations of finite Coxeter groups, J. London Math. Soc. 6 (1973), 298-300. MR 314959
  • 68. I. G. Macdonald, Symmetric functions and Hall polynomials (to appear).
  • 69. Percy Alexander MacMahon, Collected papers. Vol. I, MIT Press, Cambridge, Mass.-London, 1978. Combinatorics; Mathematicians of Our Time; Edited and with a preface by George E. Andrews; With an introduction by Gian-Carlo Rota. MR 514405
  • 70. A. O. Morris, Projective representations of Abelian groups, J. London Math. Soc. 7 (1973), 235-238. MR 327885
  • 71. A. O. Morris, Projective characters of exceptional Weyl groups, J. Algebra 29 (1974), 567-586. MR 344330
  • 72. A. O. Morris, Projective representations of Weyl groups, J. London Math. Soc. 8 (1974), 125-133. MR 338149
  • 73. A. O. Morris and J. W. Davis, The Schur multiplier of the generalized symmetric group, J. London Math. Soc. 8 (1974), 615-620. MR 347987
  • 74. A. O. Morris, Projective representations of reflection groups, Proc. London Math. Soc. 32 (1976), 403-420. MR 486086
  • 75. D. Mumford, Geometric invariant theory, Ergebnisse der Mathematik und ihrer Grenzgebiete, band 34, Academic Press, New York, 1965. MR 214602
  • 76. F. D. Murnaghan, The theory of group representations, Johns Hopkins Press, Baltimore, Md., 1938.
  • 77. T. Nakayama, On some modular properties of irreducible representations of a symmetric group. I, Japan J. Math. 17 (1940), 165-184. MR 5729
  • 78. T. Nakayama, On some modular properties of irreducible representations of a symmetric group. II, Japan J. Math. 17 (1940), 411-423. MR 5730
  • 79. T. V. Narayana, Sur les treillis formés par les partitions d'un entier et leurs applications a la théories des probabilités, C. R. Acad. Sci. Paris Sér. A 240 (1955), 1188-1189. MR 70648
  • 80. T. V. Narayana, A partial order and its applications to probability theory, Sankhyā 21 (1959), 91-98. MR 106498
  • 81. T. V. Narayana, A generalization of ballot theorems (abstract), Ann. Math. Statist. 33 (1962), 821.
  • 82. T. V. Narayana, (editor), Proceedings of the Alfred Young Day Conference, Waterloo, June 2, 1978.
  • 83. W. E. Palke, Electronic structure of LiH according to a generalization of the valence bond method, J. Chem. Phys. 50 (1969), 4524-4532.
  • 84. V. Prelog, Chirality in Chemistry, Science 193 (1976), July, pp. 17-24.
  • 85. B. M. Puttaswamaiah, On the reduction of permutation representations, Canad. Math. Bull. 6 (1963), 385-395. MR 158938
  • 86. B. M. Puttaswamaiah and G. deB. Robinson, Induced representations and alternating groups, Canad. J. Math. 16 (1964), 587-601. MR 167542
  • 87. B. M. Puttaswamaiah, Unitary representations of generalized symmetric groups, Canad. J. Math. 21 (1969), 28-38. MR 237669
  • 88. G. de B. Robinson, On the Representations of the Symmetric Group, Amer. J. Math. 60 (1938), no. 3, 745–760. MR 1507943, https://doi.org/10.2307/2371609
  • 89. G. de B. Robinson, On the representations of the symmetric group. II, Amer. J. Math. 69 (1947), 286-298. MR 20557
  • 90. G. de B. Robinson, On the representations of the symmetric group. III, Amer. J. Math. 70 (1948), 277-294. MR 29905
  • 91. G. de B. Robinson, Representation theory of the symmetric group, Univ. of Toronto Press, Toronto, 1961. MR 125885
  • 92. G. de B. Robinson, The papers of Alfred Young, Combinatoire et Représentation du Groupe Symétrique, Lecture Notes in Math., vol. 579, 1977, pp. 11-28. MR 437276
  • 93. G. de B. Robinson, Alfred Young as I knew him, Proceedings of the Alfred Young Day Conference, Waterloo, June 2, 1978, T. V. Narayana (editor).
  • 94. G.-C. Rota, Combinatorial theory and invariant theory, Notes by L. Guibas, Bowdoin College, Maine, 1971.
  • 95. G.-C. Rota, P. Doubilet and J. Stein, On the foundations of combinatorial theory. IX: combinatorial methods in invariant theory, Studies in Appl. Math. 53 (1974), 185-216. MR 498650
  • 96. G.-C. Rota, J. Desarmenien, and J. P. S. Kung, Invariant theory, Young bitableaux, and combinatorics, Advances in Math. 27 (1968), 63-92. MR 485944
  • 97. E. Ruch and A. Schönhofer, Theorie der Chiralitätsfunktionen, Theoret. Chim. Acta (Berlin) 19 (1970), 225-287.
  • 98. E. Ruch, The diagram lattice as structural principle, Theoret. Chim. Acta (Berlin) 38 (1975), 167-183. MR 503057
  • 99. E. Ruch and A. Mead, The principle of increasing mixing character and some of its consequences, Theoret. Chim. Acta (Berlin) 41 (1976), 95-117.
  • 100. D. E. Rutherford, Substitutional analysis, Edinburgh Univ. Press, Edinburgh, 1948 (reprinted: Hafner, New York, 1968). MR 27272
  • 101. C. Schensted, Longest increasing and decreasing subsequences, Canad. J. Math. 13 (1961), 179-191. MR 121305
  • 102. I. J. Schur, Neue Begründung der Theorie Gruppencharaktere, Sitz. Preuss. Akad (1905), 406-432.
  • 103. I. J. Schur, Vorlesungen über Invarianttheorie, Springer-Verlag, Berlin and New York, 1968. MR 229674
  • 104. M.-P. Schützenberger, Quelques remarques sur une construction de Schensted, Math. Scand. 12 (1963), 117-128. MR 190017
  • 105. M.-P. Schützenberger, La correspondance de Robinson, Combinatoire et Représentation du Groupe Symétrique, Lecture Notes in Math., vol. 579, 1977, pp. 59-113. MR 498826
  • 106. B. Schwarz, Rearrangements of square matrices with nonnegative elements, Duke Math. J. 31 (1964), 45-62. MR 157980
  • 107. R. P. Stanley, Theory and application of plane partitions. I, Studies in Appl. Math. 50 (1971), 167-188. MR 325407
  • 108. R. P. Stanley, Theory and application of plane partitions. II, Studies in Appl. Math. 50 (1971), 259-279. MR 325407
  • 109. G. P. Steck, A new formula for $P(R\sbiłeq b\sbi,\,1łeq iłeq mm,\,n,\,F=G\spk)$, Ann. Probability 2 (1974), 155-160.
  • 110. G. P. Steck, Lattice paths and accelerated life testing, Proceedings of the Alfred Young Day Conference, Waterloo, June 2, 1978, T. V. Narayana (editor).
  • 111. G. P. Thomas, Frames, Young tableaux and Baxter sequences, Advances in Math. 26 (1977), 275-289. MR 480065
  • 112. G. P. Thomas, Further results on Baxter sequences and generalized Schur functions, Combinatoire et Représentation du Groupe Symétrique, Lecture Notes in Math., vol. 579, Springer-Verlag, Berlin and New York, 1977, pp. 155-167. MR 472546
  • 113. G. P. Thomas, On a construction of Schützenberger, Discrete Math. 17 (1977), 107-118. MR 450084
  • 114. J. Towber, Two new functors from modules to algebras, J. Algebra 47 (1977), 80-104. MR 469955
  • 115. J. Towber, Transvection and the flag manifold, Proceedings of the Alfred Young Day Conference, Waterloo, June 2, 1978, T. V. Narayana (editor).
  • 116. H. W. Turnbull, The theory of determinants, matrices and invariants, Blackie, London, 1928.
  • 117. G. Viennot, Une forme geometrique de la correspondance de Robinson-Schensted, Combinatoire et Représentation du Groupe Symétrique, Lecture Notes in Math., vol. 579, Springer-Verlag, Berlin and New York, 1977, pp. 29-58. MR 470059
  • 118. 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
  • 119. N. White, The bracket ring of a combinatorial geometry. I, Trans. Amer. Math. Soc. 202 (1975), 79-95. MR 387095
  • 120. N. White, The bracket ring of a combinatorial geometry. II: Unimodular geometries, Trans. Amer. Math. Soc. 214 (1975), 233-248. MR 447023
  • 121. E. P. Wigner, Symmetric principles in old and new physics, Bull. Amer. Math. Soc. 74 (1968), 793-815.

Review Information:

Reviewer: George E. Andrews
Journal: Bull. Amer. Math. Soc. 1 (1979), 989-997
DOI: https://doi.org/10.1090/S0273-0979-1979-14710-4
American Mathematical Society