Weylʼs dimension formula for modules of simple inner Lie triple systems

In 2002, T.L. Hodge and B.J. Parshall [7], overviewed the representation theory of Lie triple systems (Lts for short). They proved that finite-dimensional modules of Lts in the sense of Harris (1961) [5] can be described by using involutory modules of their universal enveloping Lie algebra. The main goal of this paper is to explore the dimension of irreducible modules for simple Lts through dimensional formulas based on the remarkable Weyl formula of irreducible modules of simple Lie algebras. The paper also includes the complete classification of one-dimensional modules in arbitrary characteristic. These modules are the infinitesimal analog of symmetric line bundles.