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

Jordan Algebraic Interpretation of Maximal Parabolic Subalgebras : Exceptional Lie Algebras