  In this work, we focus on an infinite horizon mean-field linear-quadratic
stochastic control problem with jumps. Firstly, the infinite horizon linear
mean-field stochastic differential equations and backward stochastic
differential equations with jumps are studied to support the research of the
control problem. The global integrability properties of their solution
processes are studied by introducing a kind of so-called dissipation conditions
suitable for the systems involving the mean-field terms and jumps. For the
control problem, we conclude a sufficient and necessary condition of open-loop
optimal control by the variational approach. Besides, a kind of infinite
horizon fully coupled linear mean-field forward-backward stochastic
differential equations with jumps is studied by using the method of
continuation. Such a research makes the characterization of the open-loop
optimal controls more straightforward and complete.
