  With this paper we start a programme aiming at connecting two vast scientific
areas: Jordan algebras and representation theory. Within representation theory,
we focus on non-compact, real forms of semisimple Lie algebras and groups as
well as on the modern theory of their induced representations, in which a
central role is played by the parabolic subalgebras and subgroups. The aim of
the present paper and its sequels is to present a Jordan algebraic
interpretations of maximal parabolic subalgebras. In this first paper, we
confine ourselves to maximal parabolic subalgebras of the non-compact real
forms of finite-dimensional exceptional Lie algebras, in particular focusing on
Jordan algebras of rank 2 and 3.
