Abstract
In the representation theory of a compact group K, a major role is played by the Peter-Weyl theorem, which asserts that the regular representation L 2(K) decomposes as a countable direct sum of irreducibles with finite multiplicity. For compact connected Lie groups this becomes much more concrete: the irreducibles are explicitly known, their characters are given by the famous Hermann Weyl formula, and there is a uniform geometrical construction for them due to Borel and Weil.
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