  This paper studies the geometric and algebraic aspects of the moduli spaces
of quivers of fence type. We first provide two quotient presentations of the
quiver varieties and interpret their equivalence as a generalized
Gelfand-MacPherson correspondence. Next, we introduce parabolic quivers and
extend the above from the actions of reductive groups to the actions of
parabolic subgroups. Interestingly, the above geometry finds its natural
counterparts in the representation theory as the branching rules and transfer
principle in the context of the reciprocity algebra. The last half of the paper
establishes this connection.
