Leeds algebra grad course 2008

Representation theory of finite dimensional algebras, with examples


Leeds Maths.

Useful references on representation theory of the symmetric group

Partly taken from the excellent list here
[] means I have a copy.

References

[] I. Assem et al, Elements of the representation theory of associative algebras, 1 LMSST 65 Lecture Notes, CUP, 2006.
K. Baclawski, Combinatorial algorithms for Young tableaux, Lecture Notes, Univ. of California, San Diego, 1980.
[] H. Boerner, Representations of groups, 2nd ed., North-Holland, Amsterdam, 1967, 1970.
R. Brauer, On a conjecture by Nakayama, Trans. Roy. Soc. Canada Sect. III (3) 41 (1947), 11-19.

R. W. Carter and G. Lusztig, On the modular representations of the general linear and symmetric groups, Math. Z. 136 (1974), 193-242.
J-Q Chen, Group representation theory for Physicists. World Scientific, Singapore (1989).
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.
[] C. W. Curtis and I. Reiner, Representation theory of finite groups and associative algebras, vol. 11, Wiley, New York, London, Sydney, 1962.

J. Désarménian, J. P. S. Kung and G. -C. Rota, Invariant theory, Young bitableaux and combinatorics, Adv. in Math. 27 (1978), 63-92.
L. Dornhoff, Group representation theory, Part B, Dekker, New York, 1972.
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.
N. Esper, Tables of reduction of symmetrized inner products ('inner plethysms') of ordinary irreducible representations of symmetric groups, Math. Comp. 29 (1975), 1150-1151.

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. Alg. 40 (1976), 354-363.
R. H. Farrell, Techniques of multivariate calculation, Lecture Notes in Math., vol. 520, Springer-Verlag, Berlin and New York, 1976.
W. Feit, The representation theory of finite groups, North-Holland, New York, 1981.
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.

H. Garnir, Théorie de la représentation lineaire des groupes symétriques, Mem. Soc. Roy. Sci. Liege (4) 10 (1950), no. 2, 5-100.
[] J. A. Green, Polynomial representations of GLn, Lecture Notes in Math., vol. 830, Springer-Verlag, Berlin and New York, 1980.

[] M. Hamermesh, Group theory and its applications to physical problems, Addison-Wesley, Reading, Mass., 1962.
G. Higman, Representations of general linear groups and varieties of p-groups, Proc. Internat. Conf. Theory of Groups Canberra, 1965, pp. 167-173.
P. Hoffman, λ-rings and wreath product representations, Lecture Notes in Math., vol. 746, Springer-Verlag, Berlin and New York, 1979.

I. M. Isaacs, Character theory of finite groups, Academic Press, New York, San Francisco, London, 1976.

G. D. James, The representation theory of the symmetric groups, Lecture Notes in Math., vol. 682, Springer-Verlag, Berlin and New York, 1978.

A. Kerber, Representations of permutation groups. I, II, Lecture Notes in Math., vols. 240, 495, Springer-Verlag, Berlin and New York, 1971, 1975.
A. Kerber and M. H. Peel, On the decomposition numbers of symmetric and alternating groups, Mitt. Math. Sem. Univ. Giessen 91 (1971), 45-81.
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.

W. Ledermann, Introduction to group characters, Cambridge Univ. Press, London, New York, 1977.
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. (A) 239 (1944), 305-365.
D. E. Littlewood, The theory of groups, characters and matrix representations of groups, 2nd ed., Clarendon Press, Oxford, 1950.
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 Univ. Press, London and New York, 1979.
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.
[] F. D. Murnaghan, The theory of group representations, The Johns Hopkins Press, 1938.

T. Nakayama, On some modular properties of irreducible representations of a symmetric group. II, Japan J. Math. 17 (1940), 411-423.
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.
M. H. Peel, Modular representations of the symmetric groups, Univ. of Calgary Research Paper No. 292, 1975.
M. H. Peel, Specht modules and the symmetric groups, J. Algebra 36 (1975), 88-97.
39. B. M. Puttaswamaiah and J. D. Dixon, Modular representations of finite groups, Academic Press, New York, San Francisco, London, 1977.
Zentralblatt MATH: 0391.20004
Mathematical Reviews (MathSciNet): MR442071
40. G. de B. Robinson, On the representations of the symmetric group. Amer. J. Math. 60 (1938), 745-7860.
Jahrbuch database (Zbl): 64.0070.01
Mathematical Reviews (MathSciNet): MR1507943
41. G. de B. Robinson, On a conjecture by Nakayama, Trans. Roy. Soc., Canada Sect. III (3) 41 (1947), 20-25.
Zentralblatt MATH: 0029.19905
Mathematical Reviews (MathSciNet): MR29907
42. G. de B. Robinson, Representation theory of the symmetric group, Mathematical Expositions No. 12, Univ. of Toronto Press, Toronto, 1961.
Zentralblatt MATH: 0102.02002
Mathematical Reviews (MathSciNet): MR125885
43. D. E. Rutherford, Substitutional analysis, University Press, Edinburgh, 1948.
Zentralblatt MATH: 0038.01602
Mathematical Reviews (MathSciNet): MR27272
44. G. Schensted, Longest increasing and decreasing subsequences, Canad. J. Math. 13 (1961).
Zentralblatt MATH: 0097.25202
Mathematical Reviews (MathSciNet): MR121305
45. W. Specht, Die irreduziblen Darstellungen der symmetrischen Gruppe, Math. Z. 39 (1935), 696-711.
Jahrbuch database (Zbl): 61.0109.02
Mathematical Reviews (MathSciNet): MR1545531
46. G. P. Thomas, On Schensted 's construction and the multiplication of Schur-functions, Adv. in Math. 30 (1978), 8-32.
Zentralblatt MATH: 0408.05004
Mathematical Reviews (MathSciNet): MR511739
47. R. M. Thrall, On symmetrized Kronecker powers and the structure of the free Lie ring, Amer. J. Math. 64 (1942), 371-388.
Zentralblatt MATH: 0061.04201
Mathematical Reviews (MathSciNet): MR6149
48. J. Towber, Two new functors from modules to algebras, J. Algebra 47 (1977), 80-104.
Zentralblatt MATH: 0358.15033
Mathematical Reviews (MathSciNet): MR469955
49. J. Towber, Young symmetry, the flag manifold, and representations of GL(n), J. Algebra 61 (1979), 414-462.
Zentralblatt MATH: 0437.14030
Mathematical Reviews (MathSciNet): MR559849
50. H. Weyl, The classical groups, their invariants and representations, Princeton Univ. Press, Princeton, N. J., 1939.
Zentralblatt MATH: 1024.20502
Mathematical Reviews (MathSciNet): MR1488158
51. A. Young, Collected papers, Mathematical Expositions No. 21, Univ. of Toronto Press, Toronto, 1977.
Zentralblatt MATH: 0362.01007
Mathematical Reviews (MathSciNet): MR439548
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.
Zentralblatt MATH: 0465.20009
Mathematical Reviews (MathSciNet): MR643482
53. A. V. Zelevinsky, A generalization of the Littlewood-Richardson rule and the Robinson-Schenutel-Knuth correspondence, J. Algebra 69 (1981), 82-94.
Zentralblatt MATH: 0464.20010
Mathematical Reviews (MathSciNet): MR613858

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