The zero-t_0 limit of deformed hyperoctahedral q-Whittaker functions

Let $n\geq1$, and let the deformed hyperoctahedral $q$-Whittaker function depend on the parameter $t_0$. Let $\mathcal{P}^{(n)}$ be the polynomial defined by the recursion in. Zero-parameter limit conjecture. As $t_0\to0$, the deformed hyperoctahedral $q$-Whittaker function converges to the polynomial $\mathcal{P}^{(n)}$. The paper proves convergence in some special cases of the partitions involved, but leaves the general assertion conjectural.