  We give a physical realization of the Bala-Carter labels that classify
nilpotent orbits of semi-simple Lie algebras, for the case
$\mathfrak{g}=A,D,E$. We start from type IIB string theory compactified on an
$ADE$ singularity and study the six-dimensional (2,0) $\mathfrak{g}$-type
little string on a Riemann surface with punctures. The defects are introduced
as D-branes wrapping the 2-cycles of the singularity. At low energies, the
little string becomes the (2,0) conformal field theory of type $\mathfrak{g}$.
As an application, we derive the full list of $E_n$ little string defects, and
their Bala-Carter label in the CFT limit. Furthermore, we investigate new
relations between the quiver gauge theory describing the D-brane defects at low
energies, and the weighted Dynkin diagrams of $\mathfrak{g}$. We also give a
physical version of the dimension formula of a nilpotent orbit based on its
weighted Dynkin diagram.
