  Assuming the existence of an analytic interpolant mapping a two-point data
from the unit disc $\mathbb{D}$ to $\widetilde{\mathbb{G}}_n$, we describe a
class of such interpolating functions where $$\widetilde{\mathbb{G}}_n := \{
(y_1,\dots, y_{n-1}, q)\in \mathbb{C}^n :\; q \in \mathbb{D},\; y_{j} =
\beta_{j} + \bar{\beta}_{n-j} q,\; \beta_{j} \in \mathbb{C} \; \text{ and } \;
|\beta_{j}|+ |\beta_{n-j}| < {n \choose j} \; \text{ for } \; j=1,\dots, n-1
\}.$$ We present the connection of $\widetilde{\mathbb{G}}_n$ with the
$\mu$-synthesis problem.
