Jordan Algebraic Interpretation of Maximal Parabolic Subalgebras : Exceptional Lie Algebras
arXiv:1905.00289 · doi:10.1088/1751-8121/ab5f84
Abstract
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.
53 pages, V2: added Table of Contents, minor editing
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