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In this paper, we construct the quasi-normal modes of three-dimensionalextremal black holes in an algebraic way. We show that the infinite towers ofthe quasi-normal modes of scalar, vector and tensor could be constructed as thedescendents of the highest weight modes. Our investigation shows that thehidden conformal symmetry suggested in arXiv:1007.4269 is an intrinsic propertyof the extremal black hole. Moreover, we notice that we need to fix the freedomin defining the local vector fields and find the right hidden conformalsymmetry to obtain the physical quasi-normal modes.

Quasi-normal Modes of Extremal Black Holes from Hidden Conformal Symmetry