Invariant Forms on Lie Groups
In the representation theory of finite groups it often is necessary to perform summations over the elements of the group. (See Miller, Chapter 3 or Wigner , Chapter 9.) For example, the orthogonality relations for the representations and their characters are expressed as sums over the group. In order to generalize the theory to continuous groups these sums must be replaced by integration with respect to an invariant measure defined on the group.
KeywordsVector Field Riemannian Manifold Invariant Measure Isometry Group Invariant Form
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