Strange identity of Freudenthal-de Vries

• 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