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- McKay_graph abstract "In mathematics, the McKay graph of a finite-dimensional representation V of a finite group G is a weighted quiver encoding the structure of the representation theory of G. Each node represents an irreducible character of G. If are irreducible representations of G then there is an arrow from to if and only if is a constituent of the tensor product . Then the weight nij of the arrow is the number of times this constituent appears in . For finite subgroups H of GL(2, C), the McKay graph of H is the McKay graph of the canonical representation of H.If G has n irreducible characters, then the Cartan matrix cV of the representation V of dimension d is defined by , where δ is the Kronecker delta. A result by Steinberg states that if g is a representative of a conjugacy class of G, then the vectors are the eigenvectors of cV to the eigenvalues , where is the character of the representation V.The McKay correspondence, named after John McKay, states that there is a one-to-one correspondence between the McKay graphs of the finite subgroups of SL(2, C) and the extended Dynkin diagrams, which appear in the ADE classification of the simple Lie Algebras.".
- McKay_graph thumbnail Affine_Dynkin_diagrams.png?width=300.
- McKay_graph wikiPageID "34080241".
- McKay_graph wikiPageRevisionID "598779098".
- McKay_graph hasPhotoCollection McKay_graph.
- McKay_graph subject Category:Representation_theory.
- McKay_graph type Abstraction100002137.
- McKay_graph type Group100031264.
- McKay_graph type LieGroups.
- McKay_graph comment "In mathematics, the McKay graph of a finite-dimensional representation V of a finite group G is a weighted quiver encoding the structure of the representation theory of G. Each node represents an irreducible character of G. If are irreducible representations of G then there is an arrow from to if and only if is a constituent of the tensor product . Then the weight nij of the arrow is the number of times this constituent appears in .".
- McKay_graph label "McKay graph".
- McKay_graph sameAs m.0hq_mvt.
- McKay_graph sameAs Q6801707.
- McKay_graph sameAs Q6801707.
- McKay_graph sameAs McKay_graph.
- McKay_graph wasDerivedFrom McKay_graph?oldid=598779098.
- McKay_graph depiction Affine_Dynkin_diagrams.png.
- McKay_graph isPrimaryTopicOf McKay_graph.
