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Restricting and Inducing on Inner Products of Representations of Finite Groups

  • G. de B. Robinson (a1)

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Of recent years the author has been interested in developing a representation theory of the algebra of representations [5; 6] of a finite group G, and dually of its classes [7]. In this paper Frobenius’ Reciprocity Theorem provides a starting point for the introduction of the inverses R-1 and I-1 of the restricting and inducing operators R and I. The condition under which such inverse operations are available is that the classes of G do not split in the subgroup Ĝ. When this condition is satisfied the application of these operations to inner products is of interest.

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References

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1. Gamba, A., Representations and classes in groups of finite order, J. Mathematical Physics 9 (1968), 186192.
2. Lomont, J. S., Applications of finite groups (Academic Press, 1959).
3. de, G. Robinson, B., Representation theory of the symmetric group (University of Toronto Press, 1961).
4. de, G. Robinson, B., Group representations and geometry, J. Math. Physics 11 (1970), 34283432.
5. de, G. Robinson, B., The algebra of representations and classes of finite groups, J. Math. Physics 12 (1971), 22122215.
6. de, G. Robinson, B., Tensor product representations, J. of Algebra 20 (1972), 118123.
7. de, G. Robinson, B., The dual of Frobenius reciprocity theorem, Can. J. Math. 25 (1972), 10511059.
8. Young, Alfred, Quantitative substitutional analysis, Proc.Lond. Math. Soc. 3 (1932), 196230.
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Restricting and Inducing on Inner Products of Representations of Finite Groups

  • G. de B. Robinson (a1)

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