Abstract
Let H be a subgroup of a group G and R a system of left coset representatives for H. Let V be a C[G]-module and let W be a sub-C[H]module of V. Recall (cf. 3.3) that the module V (or the representation V) is said to be induced by W if we have V = ⊕s∈RsW, i.e., if V is a direct sum of the images sW, s E R (a condition which is independent of the choice of R). This property can be reformulated in the following way: Let
be the C[G]-module obtained from W by scalar extension from C[H] to C[G]. The injection W → V extends by linearity to a C[G]-homomorphism i: W′→V.
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© 1977 Springer-Verlag, New York Inc.
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Serre, JP. (1977). Induced representations; Mackey’s criterion. In: Linear Representations of Finite Groups. Graduate Texts in Mathematics, vol 42. Springer, New York, NY. https://doi.org/10.1007/978-1-4684-9458-7_7
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DOI: https://doi.org/10.1007/978-1-4684-9458-7_7
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