Geodesic
Restricting and Inducing on Inner Products of Representations of Finite Groups
Canadian journal of mathematics, Tome 27 (1975) no. 6, pp. 1349-1354

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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 splitin the subgroup Ĝ. When this condition is satisfied the application of these operations to inner products is of interest. 
Robinson, G. de B. Restricting and Inducing on Inner Products of Representations of Finite Groups. Canadian journal of mathematics, Tome 27 (1975) no. 6, pp. 1349-1354. doi: 10.4153/CJM-1975-137-2
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