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The Dual of Frobenius' Reciprocity Theorem

Published online by Cambridge University Press:  20 November 2018

G. de B. Robinson
G. de B. Robinson*
Affiliation:
University of Toronto, Toronto, Ontario
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In two preceding papers [2; 3] the author has studied the algebras of the irreducible representations λ and the classes Ci of a finite group G. Integral representations {λ} and {Ci} 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.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 25 , Issue 5 , October 1973 , pp. 1051 - 1059
Copyright
Copyright © Canadian Mathematical Society 1973

References

1. Robinson, G. de. B., Group representations and geometry, J. Mathematical Phys. 11 (1970), 3428–32.Google Scholar
2. Robinson, G. de. B., The algebras of representations and classes of finite groups, J. Mathematical Phys. 12 (1971), 2212–2215.Google Scholar
3. Robinson, G. de. B., Tensor product representations, J. Algebra 20 (1972), 118–123.Google Scholar
4. Burnside, W., The theory of groups (Cambridge Univ. Press, Cambridge, 1910).Google Scholar
5. Gamba, A., Representations and classes in groups of finite order, J. Mathematical Phys. 9 (1968), 186–192.Google Scholar