This note is aimed at presenting a new algebraic approach to momentum-space correlators in conformal field theory. As an illustration we present a new Lie-algebraic method to compute frequency-space two-point functions for charged scalar operators of CFT 1 dual to AdS 2 black hole with constant background electric field. Our method is based on the real-time prescription of AdS/CFT correspondence, Euclideanization of AdS 2 black hole and projective unitary representations of the Lie algebra sl(2, ) ⊕ sl(2, ). We derive novel recurrence relations for Euclidean CFT 1 two-point functions, which are exactly solvable and completely determine the frequencyand charge-dependences of two-point functions. Wick-rotating back to Lorentzian signature, we obtain retarded and advanced CFT 1 two-point functions that are consistent with the known results. *