Dynamics on AdS2 and Enlargement of SL(2,R) to c=1 `cut-off Virasoro Algebra'

We consider the enhancement of SL(2,R) to Virasoro algebra in a system of N particles on AdS2. We restrict our discussion to the case of non-interacting particles, and argue that they must be treated as fermions. We find operators L_n whose commutators on the ground state, |vac>, satisfy relations that are reminisent of c=1 Virasoro algebra, provided N \geq n \geq -N. Same relations hold also on the states L_{-k}|vac>, if (N-k) \geq n \geq -(N-k). The conditions L_n^\dag = L_{-n}, and L_k|vac> = 0 for k \geq 1 are also satisfied.