Abstract
The individual entries of a matrix representation of a Lie group G are continuous functions on G. They generate the ring of representative functions. The celebrated theorem of Peter and Weyl asserts that the representative functions are dense in the space of all continuous functions. This central result is proved in §3 with the help of some functional analysis which is reviewed in §2. We devote §1 to definitions and to showing that any (left or right) G-translation invariant finite-dimensional subspace of the ring of continuous functions on G actually consists of representative functions.
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© 1985 Springer Science+Business Media New York
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Bröcker, T., tom Dieck, T. (1985). Representative Functions. In: Representations of Compact Lie Groups. Graduate Texts in Mathematics, vol 98. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-12918-0_3
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DOI: https://doi.org/10.1007/978-3-662-12918-0_3
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-05725-0
Online ISBN: 978-3-662-12918-0
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