**Abstract**: We introduce a novel type of ladder operators, which map a scalar field with a mass into another scalar field with a different mass. It is shown that such operators are constructed from closed conformal Killing vector fields $zeta^mu$ in arbitrary dimensions if $zeta^mu$ is the eigen vector of the Ricci tensor. As an example, we explicitly construct the ladder operators in $AdS_2$. It is also shown that in $AdS_n$, the ladder operators exist for any scalar field with the mass above the BF bound. Furthermore, we discuss a relation between Aretakis constants and the ladder operators.

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This seminar is supported by Portuguese Funds through the CIDMA - Centre for Research and Development in Mathematics and Applications, and the Portuguese Foundation for Science and Technology ("FCT" - Fundação para a Ciência e a Tecnologia), within the project UID/MAT/04106/2013.