In what follows I'm going to use $V_{\theta_s}$ for the little adjoint representation af a Lie algebra i.e. the representation associated with the highest short rooth $\theta_s$.
Is easy to see that simple algebras of types $B_n$, $C_n$ and $F_4$ can be found as subalgebras of respectively $D_{n+1}$ with $n>3$, $A_{2n-1}$ and $E_6$ looking at the fixed poits algebra of an opportune involution (induced by an automorphism of the Dynkin Diagram)
In this article http://arxiv.org/pdf/math/0303222.pdf the autor says that if $\mathfrak{g}= \mathfrak{g}_0\oplus \mathfrak{g}_1$ is the decompoisition induced by the involution as above, then $\mathfrak{g}_1$ is isomorphic to the $\mathfrak{g}_0$-module $V(\theta_s)$.
Looking at the article this seems to be very esasy to prove but I have no ideas and no reference.
Any help is going to be well accepted.