Strange identity of Freudenthal-de Vries

introduction

• 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 \[m_{\Lambda}=\frac{(\Lambda+\rho)^2}{2(k+h^{\vee})}-\frac{\rho^2}{2h^{\vee}}=h_{\lambda}-\frac{c(k)}{24}\]

 

articles

• Thiel, Marko, and Nathan Williams. “Strange Expectations.” arXiv:1508.05293 [math], August 21, 2015. http://arxiv.org/abs/1508.05293.
• 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