The determinant of the Gram matrix for a Specht module. (English) Zbl 0417.20012
MSC:
| 20C30 | Representations of finite symmetric groups |
| 20C25 | Projective representations and multipliers |
| 20C05 | Group rings of finite groups and their modules (group-theoretic aspects) |
Keywords:
Specht module; symmetric group module; permutation module; Young subgroup; modular irreducible representation; Gram matrixReferences:
| [1] | James, G. D., The irreducible representations of the symmetric groups, Bull. London Math. Soc., 8, 229-232 (1976) · Zbl 0358.20019 |
| [2] | James, G. D., On a conjecture of Carter concerning irreducible Specht modules, (Math. Proc. Camb. Phil. Soc., 83 (1978)), 11-17 · Zbl 0385.05027 |
| [3] | James, G. D., The Representation Theory of the Symmetric Groups, (Lecture Notes in Mathematics, Vol. 682 (1978), Springer-Verlag: Springer-Verlag Berlin/New York) · Zbl 0393.20009 |
| [4] | Nakayama, T., On some modular properties of the irreducible representations of the symmetric groups I, Japan. J. Math., 17, 165-184 (1941) · JFM 67.0977.04 |
| [5] | Young, A., On quantitative substitutional analysis, VI, (Proc. London Math. Soc., 31 (1931)), 253-288, (2) · JFM 56.0135.02 |
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