Note About Classical Dynamics of Pure Spinor String on AdS_5 x S_5   Background
  We will discuss some properties of the pure spinor string on the AdS_5 x S_5 background. Using the classical Hamiltonian analysis we will show that the vertex operator for the massless state that is in the cohomology of the BRST charges describes on-shell fluctuations around AdS_5 x S_5 background. 
J. Kluson