parabolic subgroup

Let $G$ be a complex semi-simple Lie group. Then any subgroup $P$ of $G$ containga Borel subgroup $B$ is called parabolic. Parabolics are classified in thefollowing manner. Let $𝔤$ be the Lie algebra of $G$, $𝔥$ the unique Cartansubalgebra contained in $𝔟$, the algebra of $B$, $R$ the set of roots correspondingto this choice of Cartan, and $R^{+}$ the set of positive roots whose root spaces arecontained in $𝔟$ and let $𝔭$ be the Liealgebra of $P$. Then there exists a unique subset ${\mathrm{\Pi }}_P$ of $\mathrm{\Pi }$, the base of simpleroots associated to this choice of positive roots, such that${\{𝔟,{𝔤}_{-\alpha }\}}_{\alpha \in {\mathrm{\Pi }}_P}$ generates $𝔭$. In other words,parabolics containing a single Borel subgroup are classified by subsets of theDynkin diagram, with the empty set corresponding to the Borel, and the whole graphcorresponding to the group $G$.