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Weyl Character Formula: Mathematics, Representation Theory, Compact Group, Weight (representation theory), Hermann Weyl, Unitary Representation, Lie Algebra, Simple Module, Ring Theory - Softcover
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Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. In mathematics, the Weyl character formula in representation theory describes the characters of irreducible representations of compact Lie groups in terms of their highest weights. It is named after Hermann Weyl, who proved it in the late 1920s. By definition, the character of a representation r of G is the trace of r(g), as a function of a group element g in G. The irreducible representations in this case are all finite-dimensional (this is part of the Peter-Weyl theorem); so the notion of trace is the usual one from linear algebra. Knowledge of the character χ of r is a good substitute for r itself, and can have algorithmic content. Weyl''s formula is a closed formula for the χ, in terms of other objects constructed from G and its Lie algebra. The representations in question here are complex, and so without loss of generality are unitary representations; irreducible therefore means the same as indecomposable, i.e. not a direct sum of two subrepresentations.
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- PublisherBetascript Publishing
- Publication date2010
- ISBN 10 6130366183
- ISBN 13 9786130366186
- BindingTapa blanda
- LanguageEnglish
- Number of pages88
- EditorSurhone Lambert M., Timpledon Miriam T., Marseken Susan F.
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