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Frobenius Symbols and the Groups S s GL(n), O(n) and Sp(n)

  • Y. J. Abramsky (a1), H. A. Jahn (a1) and R. C. King (a1)

Extract

Frobenius [2; 3] introduced the symbols

to specify partitions and the corresponding irreducible representations of the symmetric group S s .

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References

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1. Frame, J. S., Robinson, G. de B., and Thrall, R. M., The hook graphs of the symmetric group, Can. J. Math. 6 (1954), 316324.
2. Frobenius, F. G., Über die Charaktere der symmetrischen Gruppe, Sitz. Ber. Preuss. Akad., Berlin (1900), 516534.
3. Frobenius, F. G., Über die charakteristischen Einheiten der symmetrischen Gruppe, Sitz. Ber. Preuss. Akad., Berlin (1903), 328358.
4. Hamermesh, M., Group theory and its application to physical problems (Addison-Wesley, Reading, Massachusetts, 1962).
5. King, R. C., The dimensions of irreducible tensor representations of the orthogonal and symplectic groups, Can. J. Math. 23 (1971), 176188.
6. King, R. C., Modification rules and products of irreducible representations of the unitary, orthogonal and symplectic groups, J. Math. Phys. 12 (1971), 15881598.
7. Littlewood, D. E., The theory of group characters, 2nd Edition (University Press, Oxford, 1950).
8. Littlewood, D. E., Products and plethysms of characters with orthogonal, symplectic and symmetric groups, Can. J. Math. 10 (1958), 1732.
9. Newell, M. J., Modification rules for the orthogonal and symplectic groups, Proc. Roy. Irish. Acad. Sect A 54 (1951), 153163.
10. Robinson, G. de B., Representation theory of the symmetric group (The University Press, Edinburgh, 1961).
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Frobenius Symbols and the Groups S s GL(n), O(n) and Sp(n)

  • Y. J. Abramsky (a1), H. A. Jahn (a1) and R. C. King (a1)

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