  This paper is concerned with a linear-quadratic mean field Stackelberg
stochastic differential game with partial information and common noise, which
contains a leader and a large number of followers. To be specific, the
followers face a large population Nash game after the leader first announces
his strategy, while the leader will then optimize his own cost functional on
consideration of the followers' reactions. The state equation of the leader and
followers are both general stochastic differential equations, where the
diffusion terms contain both the control and state variables. However, the
followers' average state terms enter into the drift term of the leader's state
equation, reflecting that the leader's state is influenced by the followers'
states. By virtue of stochastic maximum principle with partial information and
optimal filter technique, we deduce the open-loop adapted decentralized
strategies and feedback decentralized strategies of this leader-followers
system, and demonstrate that the decentralized strategies are the corresponding
$\varepsilon$-Stackelberg-Nash equilibrium.
