翻訳と辞書 Words near each other ・ McKale River ・ McKaley Miller ・ McKamie Farmhouse ・ McKane ・ McKane v. Durston ・ McKaskle Hills ・ McKaskle v. Wiggins ・ McKay ・ McKay Bay ・ McKay Bay Nature Park ・ McKay Christensen ・ McKay Creek ・ McKay Creek Hydroelectric Power Station ・ McKay Creek National Wildlife Refuge ・ McKay Formation ・ McKay graph ・ McKay Group ・ McKay House ・ McKay Lake ・ McKay Lake (Minnesota) ・ McKay Lake (Pic River) ・ McKay McKinnon ・ McKay Meadow, California ・ McKay Range ・ McKay Reservoir ・ McKay Tower ・ McKay v R ・ McKay Valley ・ McKay's ・ McKay's approximation for the coefficient of variation Dictionary Lists mini英和辞書 mini和英辞書 Webster 1913 Latin-English FOLDOC Wikipedia English ウィキペディア

翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク McKay graph ： ウィキペディア英語版 McKay graph 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 representation of ''G''. If $\backslash chi\_i,\; \backslash chi\_j$ are irreducible representations of ''G'' then there is an arrow from $\backslash chi\_i$ to $\backslash chi\_j$ if and only if $\backslash chi\_j$ is a constituent of the tensor product $V\backslash otimes\backslash chi\_i$. Then the weight ''nij'' of the arrow is the number of times this constituent appears in $V\; \backslash otimes\backslash chi\_i$. 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 $c\_V\; =\; (d\backslash delta\_\; -n\_)\_$, 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 $((\backslash chi\_i(g))\_i$ are the eigenvectors of ''cV'' to the eigenvalues $d-\backslash chi\_V(g)$, where $\backslash chi\_V$ 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. ==Definition== Let ''G'' be a finite group, ''V'' be a representation of ''G'' and $\backslash chi$ be its character. Let $\backslash$ be the irreducible representations of ''G''. If :$$ 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「McKay graph」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.