"Strange identity of Freudenthal-de Vries"의 두 판 사이의 차이

2012년 8월 26일 (일) 17:43 판

Root Systems and Dynkin diagrams
\(\rho\) Weyl vector
Kac book 219p, 221p
strange formula
\(\frac{<\rho,\rho>}{2h^{\vee}}=\frac{\operatorname{dim}\mathfrak{g}}{24}\)
very strange formula
conformal anomaly
\(m_{\Lambda}=\frac{(\Lambda+\rho)^2}{2(k+h^{\vee})}-\frac{\rho^2}{2h^{\vee}}=h_{\lambda}-\frac{c(k)}{24}\)

H. FREUDENTHAL and H. DE VRIES. “Linear Lie groups”, New York: Academic Press, 1969.

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+* [[Root Systems and Dynkin diagrams]]
+* <math>\rho</math> Weyl vector
+* Kac book 219p, 221p
+*  strange formula<br><math>\frac{<\rho,\rho>}{2h^{\vee}}=\frac{\operatorname{dim}\mathfrak{g}}{24}</math><br>
+*  very strange formula<br>
+*  conformal anomaly <br><math>m_{\Lambda}=\frac{(\Lambda+\rho)^2}{2(k+h^{\vee})}-\frac{\rho^2}{2h^{\vee}}=h_{\lambda}-\frac{c(k)}{24}</math><br>
+H. FREUDENTHAL and H. DE VRIES. “Linear Lie groups”, New York: Academic Press, 1969.
+* [http://qjmath.oxfordjournals.org/cgi/reprint/51/3/295.pdf AN ELEMENTARY PROOF OF THE 'STRANGE FORMULA' OF FREUDENTHAL AND DE Vries]<br>
+**  John Burn, 2004<br>