Restriction to a subgroup
In this chapter and the next, we are going to look at ways of relating the representations of a group to the representations of its subgroups. Here, we introduce the elementary idea of restricting a G-module to a subgroup H of G, and illustrate its use. The case where H is a normal subgroup of G is of particular interest, and Clifford’s Theorem 20.8 gives important information in this case. We apply this result in the situation where H is of index 2 in G, which occurs, for example, when G = Sn and H = An.
Let H be a subgroup of the finite group G. Then H is a subset of G. If V is a G-module, then V is also ...