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The Dual of Frobenius' Reciprocity Theorem

  • G. de B. Robinson (a1)

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In two preceding papers [2; 3] the author has studied the algebras of the irreducible representations λ and the classes C i of a finite group G. Integral representations {λ} and {C i } of these algebras are derivable from the appropriate multiplication tables [4]. It should be emphasized, however, that the symmetry properties of the two sets of structure constants are not the same, and this leads to somewhat greater complexity in the formulae relating to classes as compared to representations.

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References

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1. Robinson, G. de. B., Group representations and geometry, J. Mathematical Phys. 11 (1970), 3428–32.
2. Robinson, G. de. B., The algebras of representations and classes of finite groups, J. Mathematical Phys. 12 (1971), 22122215.
3. Robinson, G. de. B., Tensor product representations, J. Algebra 20 (1972), 118123.
4. Burnside, W., The theory of groups (Cambridge Univ. Press, Cambridge, 1910).
5. Gamba, A., Representations and classes in groups of finite order, J. Mathematical Phys. 9 (1968), 186192.
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The Dual of Frobenius' Reciprocity Theorem

  • G. de B. Robinson (a1)

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