For sp(n+2) and each exceptional Lie algebra a realization of depth 2 preserving the spaces spanned by a contact one-form and a bilinear form is given. For e_7 and e_6 a realization of depth 1 preserving a lightcone and the space spanned by a bilinear form is also presented. This makes the origin of the exceptions clear.
New Structures in the Theory of the Laser Model
Quantum integrable system associated with the $G_2$ exceptional Lie algebra
Indecomposable representations and oscillator realizations of the exceptional Lie algebra G_2
