On complex weakly commutative homogeneous spaces

Let $G$ be a complex algebraic group and $L$ an algebraic subgroup of $G$. The quotient space $G/L$ is called weakly commutative if a generic orbit of the action $G:T^*(G/L)$ is a coisotropic submanifold. We classify weakly commutative homogeneous spaces $N\leftthreetimes L/L$ in the case where $L$ is a reductive group and the natural representation $L:\mathfrak{n}/[\mathfrak{n},\mathfrak{n}]$, where $\mathfrak{n}$ is the tangent algebra of the group $N$, is irreducible.