. "Weyl\u2013Kac character formula"@en . "In der Mathematik ist die Weylsche Charakterformel oder Charakterformel von Weyl eine Formel zur Berechnung des Charakters einer Darstellung aus ihrem h\u00F6chsten Gewicht. Sie wurde 1926 von Hermann Weyl bewiesen und folgt auch aus dem Atiyah-Bott-Fixpunktsatz."@de . . . . . . . "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 . There is a closely related formula for the character of an irreducible representation of a semisimple Lie algebra. In Weyl's approach to the representation theory of connected compact Lie groups, the proof of the character formula is a key step in proving that every dominant integral element actually arises as the highest weight of some irreducible representation. Important consequences of the character formula are the Weyl dimension formula and the Kostant multiplicity formula. By definition, the character of a representation of G is the trace of , as a function of a group element . The irreducible representations in this case are all finite-dimensional (this is part of the Peter\u2013Weyl theorem); so the notion of trace is the usual one from linear algebra. Knowledge of the character of gives a lot of information about itself. Weyl's formula is a closed formula for the character , in terms of other objects constructed from G and its Lie algebra."@en . "Weyl character formula"@en . . . "\uB9AC \uAD70 \uD45C\uD604\uB860\uC5D0\uC11C \uBC14\uC77C \uC9C0\uD45C \uACF5\uC2DD(Weyl\u6307\u6A19\u516C\u5F0F, \uC601\uC5B4: Weyl character formula)\uC740 \uC8FC\uC5B4\uC9C4 \uBCF5\uC18C\uC218 \uAE30\uC57D \uD45C\uD604\uC758 \uC9C0\uD45C\uB97C \uC81C\uC2DC\uD558\uB294 \uACF5\uC2DD\uC774\uB2E4."@ko . . "W/w130070"@en . "\u30EF\u30A4\u30EB\u306E\u6307\u6A19\u516C\u5F0F"@ja . . "Hermann Weyl"@en . . . . . . . . . . . "\uBC14\uC77C \uC9C0\uD45C \uACF5\uC2DD"@ko . . . . . . . . . . "5011916"^^ . . "1926"^^ . "1925"^^ . "\uB9AC \uAD70 \uD45C\uD604\uB860\uC5D0\uC11C \uBC14\uC77C \uC9C0\uD45C \uACF5\uC2DD(Weyl\u6307\u6A19\u516C\u5F0F, \uC601\uC5B4: Weyl character formula)\uC740 \uC8FC\uC5B4\uC9C4 \uBCF5\uC18C\uC218 \uAE30\uC57D \uD45C\uD604\uC758 \uC9C0\uD45C\uB97C \uC81C\uC2DC\uD558\uB294 \uACF5\uC2DD\uC774\uB2E4."@ko . . . "\u5916\u5C14\u7279\u5FB5\u6A19\u516C\u5F0F\uFF08Weyl's character formula) \u63CF\u8FF0\u7DCA\u674E\u7FA3\u4E0D\u53EF\u7D04\u8868\u793A\u7684\u7279\u5FB5\u6A19\u3002\u5176\u540D\u4F86\u81EA\u8B49\u660E\u8005\u8D6B\u5C14\u66FC\u00B7\u5916\u5C14\u3002 \u5B9A\u7FA9\uFF1A\u7FA3G\u7684\u8868\u793Ar\u7684\u7279\u5FB5\u6A19\u70BA\u4E00\u51FD\u6578 \uFF0C\uFF0C\u5176\u4E2DTr \u70BA\u7DDA\u6027\u7B97\u5B50\u4E4B\u8FF9\u3002 \uFF08\u7531\u5F7C\u5F97-\u5916\u5C14\u5B9A\u7406 \u53EF\u77E5\u7DCA\u674E\u7FA3\u7684\u4EFB\u4F55\u4E0D\u53EF\u7D04\u8868\u793A\u90FD\u662F\u6709\u9650\u7DAD\u7684\uFF1B\u6545\u8FF9\u4E4B\u5B9A\u7FA9\u70BA\u7DDA\u6027\u4EE3\u6578\u4E2D\u4E4B\u5B9A\u7FA9\u3002\uFF09 \u7279\u5FB5\u6A19 \u03C7 \u8A18\u4F4F\u4E86\u8868\u793A r \u672C\u8EAB\u7684\u91CD\u8981\u8A0A\u606F\u3002 \u5916\u5C14\u7279\u5FB5\u6A19\u516C\u5F0F\u7528\u7FA3G\u7684\u5176\u4ED6\u8CC7\u6599\u4F86\u8868\u9054 \u03C7 \u3002 \u672C\u6587\u8003\u616E\u8907\u8868\u793A\uFF0C\u4E0D\u5931\u4E00\u822C\u4EA6\u8A2D\u5176\u70BA\uFF0C\u56E0\u800C\u300C\u4E0D\u53EF\u7D04\u300D\u4EA6\u7B49\u50F9\u65BC\u300C\u4E0D\u53EF\u5206\u89E3\u300D\uFF08\u5373\u975E\u4E8C\u5B50\u8868\u793A\u4E4B\u76F4\u548C\uFF09\u3002"@zh . "Duncan J. Melville"@en . . . . . . "\u5916\u5C14\u7279\u5FB5\u6A19\u516C\u5F0F\uFF08Weyl's character formula) \u63CF\u8FF0\u7DCA\u674E\u7FA3\u4E0D\u53EF\u7D04\u8868\u793A\u7684\u7279\u5FB5\u6A19\u3002\u5176\u540D\u4F86\u81EA\u8B49\u660E\u8005\u8D6B\u5C14\u66FC\u00B7\u5916\u5C14\u3002 \u5B9A\u7FA9\uFF1A\u7FA3G\u7684\u8868\u793Ar\u7684\u7279\u5FB5\u6A19\u70BA\u4E00\u51FD\u6578 \uFF0C\uFF0C\u5176\u4E2DTr \u70BA\u7DDA\u6027\u7B97\u5B50\u4E4B\u8FF9\u3002 \uFF08\u7531\u5F7C\u5F97-\u5916\u5C14\u5B9A\u7406 \u53EF\u77E5\u7DCA\u674E\u7FA3\u7684\u4EFB\u4F55\u4E0D\u53EF\u7D04\u8868\u793A\u90FD\u662F\u6709\u9650\u7DAD\u7684\uFF1B\u6545\u8FF9\u4E4B\u5B9A\u7FA9\u70BA\u7DDA\u6027\u4EE3\u6578\u4E2D\u4E4B\u5B9A\u7FA9\u3002\uFF09 \u7279\u5FB5\u6A19 \u03C7 \u8A18\u4F4F\u4E86\u8868\u793A r \u672C\u8EAB\u7684\u91CD\u8981\u8A0A\u606F\u3002 \u5916\u5C14\u7279\u5FB5\u6A19\u516C\u5F0F\u7528\u7FA3G\u7684\u5176\u4ED6\u8CC7\u6599\u4F86\u8868\u9054 \u03C7 \u3002 \u672C\u6587\u8003\u616E\u8907\u8868\u793A\uFF0C\u4E0D\u5931\u4E00\u822C\u4EA6\u8A2D\u5176\u70BA\uFF0C\u56E0\u800C\u300C\u4E0D\u53EF\u7D04\u300D\u4EA6\u7B49\u50F9\u65BC\u300C\u4E0D\u53EF\u5206\u89E3\u300D\uFF08\u5373\u975E\u4E8C\u5B50\u8868\u793A\u4E4B\u76F4\u548C\uFF09\u3002"@zh . . . . . . . . . "Weylsche Charakterformel"@de . . . "1084905278"^^ . . . . . . . . "\u6570\u5B66\u306B\u304A\u3044\u3066\uFF0C\u8868\u73FE\u8AD6\u306B\u304A\u3051\u308B\u30EF\u30A4\u30EB\u306E\u6307\u6A19\u516C\u5F0F\uFF08\u82F1: Weyl character formula\uFF09\u306F\u30B3\u30F3\u30D1\u30AF\u30C8\u30EA\u30FC\u7FA4\u306E\u65E2\u7D04\u8868\u73FE\u306E\u6307\u6A19\u3092\u306E\u3053\u3068\u3070\u3067\u8A18\u8FF0\u3059\u308B\uFF0EHermann Weyl \u306B\u3088\u3063\u3066\u8A3C\u660E\u3055\u308C\u305F\uFF0E \u5B9A\u7FA9\u306B\u3088\u308A\uFF0CG \u306E\u8868\u73FE r \u306E\u6307\u6A19\u306F\u7FA4 G \u306E\u5143 g \u306E\u95A2\u6570\u3068\u3057\u3066\u306E r(g) \u306E\u30C8\u30EC\u30FC\u30B9\u3067\u3042\u308B\uFF0E\u3053\u306E\u5834\u5408\u65E2\u7D04\u8868\u73FE\u306F\u3059\u3079\u3066\u6709\u9650\u6B21\u5143\u3067\u3042\u308B\uFF08\u3053\u308C\u306F\u306E\u4E00\u90E8\u3067\u3042\u308B\uFF09\uFF0E\u3088\u3063\u3066\u30C8\u30EC\u30FC\u30B9\u306E\u6982\u5FF5\u306F\u7DDA\u578B\u4EE3\u6570\u5B66\u306E\u901A\u5E38\u306E\u3082\u306E\u3067\u3042\u308B\uFF0Er \u306E\u6307\u6A19 \u03BE \u3092\u77E5\u308B\u3053\u3068\u306F r \u81EA\u8EAB\u306E\u826F\u3044\u4EE3\u66FF\u3067\u3042\u308A\uFF0C\u30A2\u30EB\u30B4\u30EA\u30BA\u30E0\u7684\u5185\u5BB9\u3092\u6301\u3061\u5F97\u308B\uFF0E\u30EF\u30A4\u30EB\u306E\u516C\u5F0F\u306F G \u304B\u3089\u69CB\u6210\u3055\u308C\u308B\u4ED6\u306E\u5BFE\u8C61\u3068 G \u306E\u30EA\u30FC\u74B0\u306E\u3053\u3068\u3070\u3067 \u03BE \u3092\u3067\u8868\u3059\uFF0E\u3053\u3053\u3067\u554F\u984C\u306E\u8868\u73FE\u306F\u8907\u7D20\u3067\u3042\u308A\u3057\u305F\u304C\u3063\u3066\u4E00\u822C\u6027\u3092\u5931\u3046\u3053\u3068\u306A\u304F\u30E6\u30CB\u30BF\u30EA\u8868\u73FE\u3067\u3042\u308B\uFF1B\u3057\u305F\u304C\u3063\u3066\u65E2\u7D04\u306F\u76F4\u65E2\u7D04\uFF0C\u3064\u307E\u308A2\u3064\u306E\u90E8\u5206\u8868\u73FE\u306E\u76F4\u548C\u3067\u306A\u3044\u3053\u3068\u3068\u540C\u3058\u610F\u5473\u3067\u3042\u308B\uFF0E"@ja . . "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 . There is a closely related formula for the character of an irreducible representation of a semisimple Lie algebra. In Weyl's approach to the representation theory of connected compact Lie groups, the proof of the character formula is a key step in proving that every dominant integral element actually arises as the highest weight of some irreducible representation. Important consequences of the character formula are the Weyl dimension formula and the Kostant multiplicity formula."@en . . . "Weyl"@en . "\u5916\u5C14\u7279\u5F81\u6807\u516C\u5F0F"@zh . "19888"^^ . . "\u6570\u5B66\u306B\u304A\u3044\u3066\uFF0C\u8868\u73FE\u8AD6\u306B\u304A\u3051\u308B\u30EF\u30A4\u30EB\u306E\u6307\u6A19\u516C\u5F0F\uFF08\u82F1: Weyl character formula\uFF09\u306F\u30B3\u30F3\u30D1\u30AF\u30C8\u30EA\u30FC\u7FA4\u306E\u65E2\u7D04\u8868\u73FE\u306E\u6307\u6A19\u3092\u306E\u3053\u3068\u3070\u3067\u8A18\u8FF0\u3059\u308B\uFF0EHermann Weyl \u306B\u3088\u3063\u3066\u8A3C\u660E\u3055\u308C\u305F\uFF0E \u5B9A\u7FA9\u306B\u3088\u308A\uFF0CG \u306E\u8868\u73FE r \u306E\u6307\u6A19\u306F\u7FA4 G \u306E\u5143 g \u306E\u95A2\u6570\u3068\u3057\u3066\u306E r(g) \u306E\u30C8\u30EC\u30FC\u30B9\u3067\u3042\u308B\uFF0E\u3053\u306E\u5834\u5408\u65E2\u7D04\u8868\u73FE\u306F\u3059\u3079\u3066\u6709\u9650\u6B21\u5143\u3067\u3042\u308B\uFF08\u3053\u308C\u306F\u306E\u4E00\u90E8\u3067\u3042\u308B\uFF09\uFF0E\u3088\u3063\u3066\u30C8\u30EC\u30FC\u30B9\u306E\u6982\u5FF5\u306F\u7DDA\u578B\u4EE3\u6570\u5B66\u306E\u901A\u5E38\u306E\u3082\u306E\u3067\u3042\u308B\uFF0Er \u306E\u6307\u6A19 \u03BE \u3092\u77E5\u308B\u3053\u3068\u306F r \u81EA\u8EAB\u306E\u826F\u3044\u4EE3\u66FF\u3067\u3042\u308A\uFF0C\u30A2\u30EB\u30B4\u30EA\u30BA\u30E0\u7684\u5185\u5BB9\u3092\u6301\u3061\u5F97\u308B\uFF0E\u30EF\u30A4\u30EB\u306E\u516C\u5F0F\u306F G \u304B\u3089\u69CB\u6210\u3055\u308C\u308B\u4ED6\u306E\u5BFE\u8C61\u3068 G \u306E\u30EA\u30FC\u74B0\u306E\u3053\u3068\u3070\u3067 \u03BE \u3092\u3067\u8868\u3059\uFF0E\u3053\u3053\u3067\u554F\u984C\u306E\u8868\u73FE\u306F\u8907\u7D20\u3067\u3042\u308A\u3057\u305F\u304C\u3063\u3066\u4E00\u822C\u6027\u3092\u5931\u3046\u3053\u3068\u306A\u304F\u30E6\u30CB\u30BF\u30EA\u8868\u73FE\u3067\u3042\u308B\uFF1B\u3057\u305F\u304C\u3063\u3066\u65E2\u7D04\u306F\u76F4\u65E2\u7D04\uFF0C\u3064\u307E\u308A2\u3064\u306E\u90E8\u5206\u8868\u73FE\u306E\u76F4\u548C\u3067\u306A\u3044\u3053\u3068\u3068\u540C\u3058\u610F\u5473\u3067\u3042\u308B\uFF0E"@ja . . "In der Mathematik ist die Weylsche Charakterformel oder Charakterformel von Weyl eine Formel zur Berechnung des Charakters einer Darstellung aus ihrem h\u00F6chsten Gewicht. Sie wurde 1926 von Hermann Weyl bewiesen und folgt auch aus dem Atiyah-Bott-Fixpunktsatz."@de . . "Hermann"@en . .