Induced representations; Mackey’s criterion

  • Jean-Pierre Serre
Part of the Graduate Texts in Mathematics book series (GTM, volume 42)


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
$$ W' = C\left[ G \right]{ \otimes _{C\left[ H \right]}}W $$
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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Copyright information

© Springer-Verlag, New York Inc. 1977

Authors and Affiliations

  • Jean-Pierre Serre
    • 1
  1. 1.Chaire d’algèbre et géométrieCollège de FranceParisFrance

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