  A group theoretical formulation of Schramm--Loewner-evolution-type growth
processes corresponding to Wess--Zumino--Witten theories is developed that
makes it possible to construct stochastic differential equations associated
with more general null vectors than the ones considered in the most fundamental
example in [Alekseev et al., Lett. Math. Phys. 97, 243-261 (2011)]. Also given
are examples of Schramm--Loewner-evolution-type growth processes associated
with null vectors of conformal weight $4$ in the basic representations of
$\widehat{\mathfrak{sl}}_{2}$ and $\widehat{\mathfrak{sl}}_{3}$.
