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Letter place algebras and a characteristic-free approach to the representation theory of the general linear and symmetric groups. I. (English) Zbl 0425.20011


MSC:

20C30 Representations of finite symmetric groups

Citations:

Zbl 0373.05010
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References:

[1] Carter, R. W.; Lusztig, G., On the modular representations of the general linear and symmetric groups, Math. Z., 136, 193-242 (1974) · Zbl 0298.20009
[2] Carter, R. W.; Lusztig, G., Modular representations of finite groups of Lie type, Proc. London Math. Soc., 32, 3, 347-384 (1976) · Zbl 0338.20013
[3] Coleman, A. J., Induced Representations with Applications to \(S_n\) and GL(n), (Queen’s Papers in Pure and Applied Mathematics (1966), Queen’s University: Queen’s University New York), No. 4 · Zbl 0141.02503
[4] Curtis, C. W.; Reiner, I., Representation Theory of Finite Groups and Associative Algebras (1962), Interscience: Interscience Kingston, Ontario · Zbl 0131.25601
[5] Désarménien, J.; Kung, J. P.S.; Rota, G.-C., Invariant theory, Young bitableaux and combinatorics, Advances in Math, 27, 63-92 (1978) · Zbl 0373.05010
[6] Doubilet, P.; Rota, G.-C.; Stein, J., On the foundations of combinatorial theory: IX. Combinatorial methods in invariant theory, Stud. Appl. Math., 53, 185-216 (1974) · Zbl 0426.05009
[7] Humphreys, J. E., (Graduate texts in Mathematics, 21 (1975), Springer-Verlag: Springer-Verlag New York/London/Sydney)
[8] Humphreys, J. E., Ordinary and Modular Representations of Chevalley groups, (Lecture Notes in Mathematics (1976), Springer-Verlag: Springer-Verlag New York/Heidelberg/Berlin), No. 528 · Zbl 0919.17013
[9] James, G. D., The irreducible representations of the symmetric groups, Bull. London Math. Soc., 8, 229-232 (1976) · Zbl 0358.20019
[10] James, G. D., A characteristic-free approach to the representation theory of \(S_n\), J. Algebra, 46, 430-450 (1977) · Zbl 0358.20011
[11] James, G. D., The Representation Theory of the Symmetric Groups, (Lecture Notes in Mathematics (1978), Springer-Verlag: Springer-Verlag Berlin/Heidelberg/New York), No. 682 · Zbl 0393.20009
[12] A. Kerber; A. Kerber
[13] Liebler, R. A.; Vitale, M. R., Ordering the partition characters of the symmetric group, J. Algebra, 25, 487-489 (1973) · Zbl 0274.20016
[14] Peel, M. H., Modular Representations of the Symmetric Groups, University of Calgary Research Paper No. 292 (1975) · Zbl 0313.20005
[15] Snapper, E., Group characters and nonnegative integral matrices, J. Algebra, 19, 520-535 (1971) · Zbl 0226.20008
[16] Thrall, R. M., On the decomposition of modular tensors, I, Ann. of Math., 43, 671-684 (1942) · Zbl 0061.04103
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