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

2012년 10월 27일 (토) 12:57 판

Root Systems and Dynkin diagrams
\(\rho\) Weyl vector
Kac book 219p, 221p
strange formula \[\frac{\langle\rho,\rho\rangle}{2h^{\vee}}=\frac{\operatorname{dim}\mathfrak{g}}{24}\]
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.
AN ELEMENTARY PROOF OF THE 'STRANGE FORMULA' OF FREUDENTHAL AND DE Vries
- John Burn, 2004

@@ 2번째 줄: / 2번째 줄: @@
 * <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>
+*  strange formula :<math>\frac{\langle\rho,\rho\rangle}{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>
+*  conformal anomaly :<math>m_{\Lambda}=\frac{(\Lambda+\rho)^2}{2(k+h^{\vee})}-\frac{\rho^2}{2h^{\vee}}=h_{\lambda}-\frac{c(k)}{24}</math><br>
@@ 12번째 줄: / 12번째 줄: @@
-H. FREUDENTHAL and H. DE VRIES. “Linear Lie groups”, New York: Academic Press, 1969.
+* 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>