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- Weyl_character_formula abstract "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 was proved by Hermann Weyl (1925, 1926a, 1926b).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.".
- Weyl_character_formula wikiPageID "5011916".
- Weyl_character_formula wikiPageLength "9476".
- Weyl_character_formula wikiPageOutDegree "40".
- Weyl_character_formula wikiPageRevisionID "679062038".
- Weyl_character_formula wikiPageWikiLink Admissible_representation.
- Weyl_character_formula wikiPageWikiLink Algebraic_character.
- Weyl_character_formula wikiPageWikiLink Analytic_function.
- Weyl_character_formula wikiPageWikiLink Cartan_subalgebra.
- Weyl_character_formula wikiPageWikiLink Cartan_subgroup.
- Weyl_character_formula wikiPageWikiLink Category:Representation_theory_of_Lie_groups.
- Weyl_character_formula wikiPageWikiLink Character_(mathematics).
- Weyl_character_formula wikiPageWikiLink Closed-form_expression.
- Weyl_character_formula wikiPageWikiLink Closed_formula.
- Weyl_character_formula wikiPageWikiLink Compact_Lie_group.
- Weyl_character_formula wikiPageWikiLink Compact_group.
- Weyl_character_formula wikiPageWikiLink Demazure_character_formula.
- Weyl_character_formula wikiPageWikiLink Demazure_module.
- Weyl_character_formula wikiPageWikiLink Elliptic_modular_function.
- Weyl_character_formula wikiPageWikiLink Generalized_Kac–Moody_algebra.
- Weyl_character_formula wikiPageWikiLink Hans_Freudenthal.
- Weyl_character_formula wikiPageWikiLink Harish-Chandra_character.
- Weyl_character_formula wikiPageWikiLink Highest_weight.
- Weyl_character_formula wikiPageWikiLink Infinitesimal_character.
- Weyl_character_formula wikiPageWikiLink Irreducible_representation.
- Weyl_character_formula wikiPageWikiLink J-invariant.
- Weyl_character_formula wikiPageWikiLink Jacobi_triple_product.
- Weyl_character_formula wikiPageWikiLink Kac–Moody_algebra.
- Weyl_character_formula wikiPageWikiLink Lie_algebra.
- Weyl_character_formula wikiPageWikiLink Macdonald_identities.
- Weyl_character_formula wikiPageWikiLink Mathematics.
- Weyl_character_formula wikiPageWikiLink Mathematische_Zeitschrift.
- Weyl_character_formula wikiPageWikiLink Monster_Lie_algebra.
- Weyl_character_formula wikiPageWikiLink Peter–Weyl_theorem.
- Weyl_character_formula wikiPageWikiLink Positive_root.
- Weyl_character_formula wikiPageWikiLink Rebecca_A._Herb.
- Weyl_character_formula wikiPageWikiLink Reductive_group.
- Weyl_character_formula wikiPageWikiLink Representation_theory.
- Weyl_character_formula wikiPageWikiLink Root_system.
- Weyl_character_formula wikiPageWikiLink Trace_(linear_algebra).
- Weyl_character_formula wikiPageWikiLink Trace_of_a_matrix.
- Weyl_character_formula wikiPageWikiLink Unitary_representation.
- Weyl_character_formula wikiPageWikiLink Vandermonde_determinant.
- Weyl_character_formula wikiPageWikiLink Vandermonde_matrix.
- Weyl_character_formula wikiPageWikiLink Weight_(representation_theory).
- Weyl_character_formula wikiPageWikiLink Weyl_group.
- Weyl_character_formula wikiPageWikiLink Without_loss_of_generality.
- Weyl_character_formula wikiPageWikiLinkText "Weyl character formula".
- Weyl_character_formula wikiPageWikiLinkText "Weyl character formula#Freudenthal's formula".
- Weyl_character_formula wikiPageWikiLinkText "Weyl character formula#Statement of Weyl character formula".
- Weyl_character_formula wikiPageWikiLinkText "Weyl character formula#Weyl denominator formula".
- Weyl_character_formula wikiPageWikiLinkText "Weyl character formula#Weyl dimension formula".
- Weyl_character_formula wikiPageWikiLinkText "Weyl-Kac character formula".
- Weyl_character_formula wikiPageWikiLinkText "Weyl–Kac character formula".
- Weyl_character_formula wikiPageWikiLinkText "character formula".
- Weyl_character_formula wikiPageWikiLinkText "character of a finite-dimensional representation".
- Weyl_character_formula wikiPageWikiLinkText "explicit character formulas".
- Weyl_character_formula wikiPageWikiLinkText "irreducible representation".
- Weyl_character_formula wikiPageWikiLinkText "irreducible representations".
- Weyl_character_formula wikiPageWikiLinkText "representation theory of compact semisimple groups".
- Weyl_character_formula author "Duncan J. Melville".
- Weyl_character_formula authorLink "Hermann Weyl".
- Weyl_character_formula first "Hermann".
- Weyl_character_formula hasPhotoCollection Weyl_character_formula.
- Weyl_character_formula id "W/w130070".
- Weyl_character_formula last "Weyl".
- Weyl_character_formula title "Weyl–Kac character formula".
- Weyl_character_formula wikiPageUsesTemplate Template:Citation.
- Weyl_character_formula wikiPageUsesTemplate Template:Harvs.
- Weyl_character_formula wikiPageUsesTemplate Template:Springer.
- Weyl_character_formula year "1925".
- Weyl_character_formula year "1926".
- Weyl_character_formula subject Category:Representation_theory_of_Lie_groups.
- Weyl_character_formula comment "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 was proved by Hermann Weyl (1925, 1926a, 1926b).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.".
- Weyl_character_formula label "Weyl character formula".
- Weyl_character_formula sameAs m.0czs8f.
- Weyl_character_formula sameAs Q7990328.
- Weyl_character_formula sameAs Q7990328.
- Weyl_character_formula sameAs 外爾特徵標公式.
- Weyl_character_formula wasDerivedFrom Weyl_character_formula?oldid=679062038.
- Weyl_character_formula isPrimaryTopicOf Weyl_character_formula.