O'Reilly logo

Induced Representations of Locally Compact Groups by Keith F. Taylor, Eberhard Kaniuth

Stay ahead with the world's most comprehensive technology and business learning platform.

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, tutorials, and more.

Start Free Trial

No credit card required

5.7 Examples: motion groups

The first purpose of this section is to describe the dual space topology for some motion groups to which Theorem 5.58 applies easily. Afterwards, we use Theorem 5.58 to deduce a necessary and sufficient condition for a general motion group to have a Hausdorff dual space.

Example 5.59   Let G = ℝn images SO(n), the group of rigid motions of ℝn, n ≥ 2, and let H = ℝn images SO(n – 1), where SO(n – 1) is identified with the stabilizer group of the vector (1, 0, …, 0) in SO(n). For r > 0 let χr denote the character of ℝn defined by ...

With Safari, you learn the way you learn best. Get unlimited access to videos, live online training, learning paths, books, interactive tutorials, and more.

Start Free Trial

No credit card required