Algebras of invariant functions on the Shilov boundaries of Siegel domains

Let $D=G/K$ be a bounded symmetric domain and $K/L$ the Shilov boundary of $D$. Let $\mathcal{N}$ be the Shilov boundary of the Siegel domain realization of $G/K$. We consider the case when $D$ is the exceptional non-tube type domain of the type $(\mathfrak{e}_{6(-14)}, \mathfrak{so}(10)\times \mathfrak{so}(2))$. We prove that $(\mathcal{N}\rtimes L, L)$ is not a Gelfand pair and thus resolve an open question of G. Carcano.