Representations of Locally Compact Totally Disconnected Groups
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چکیده
Let G be a locally compact totally disconnected group. Recall that every neighborhood of 1 in G contains a compact open subgroup. If G is assumed to be compact, then every neighborhood of 1 in G contains a compact open normal subgroup. On the other hand, it follows from properties of Lie groups that the group GL(n,C) has the property that there is some neighborhood of the identity which contains no nontrivial subgroups. That is, GL(n,C) has no small subgroups. This may be used to obtain the following description of finite dimensional continuous representations of compact totally disconnected groups.
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