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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

 
9786130366186: Weyl Character Formula: Mathematics, Representation Theory, Compact Group, Weight (representation theory), Hermann Weyl, Unitary Representation, Lie Algebra, Simple Module, Ring Theory
Softcover
ISBN 10: 6130366183 ISBN 13: 9786130366186
Verlag: Betascript Publishers, 2010

Inhaltsangabe

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.

Die Inhaltsangabe kann sich auf eine andere Ausgabe dieses Titels beziehen.

Reseña del editor

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.

„Über diesen Titel“ kann sich auf eine andere Ausgabe dieses Titels beziehen.

Verlag
Betascript Publishers
Erscheinungsdatum
2010
Sprache
Englisch
ISBN 10 
6130366183
ISBN 13 
9786130366186
Einband
Tapa blanda
Anzahl der Seiten
88
Herausgeber
Surhone Lambert M., Timpledon Miriam T., Marseken Susan F.
Kontakt zum Hersteller
Nicht verfügbar
Verantwortliche Person
Nicht verfügbar