The raising and lowering conjecture for q-Whittaker functions of types BCD

For a classical root system of type $D_N$, $B_N$, or $C_N$, let $M_{a,k}^{(G)}$ be the corresponding difference operators and let $\Pi_\lambda^{(G)}(q^{-1};\mathbf{x})$ be the dual $q$-Whittaker functions, with $\omega_a$ and $\alpha_a$ the fundamental weights and simple roots. Set $t_a=2$ for short roots in types $B_N$ and $C_N$, and $t_a=1$ otherwise. Raising and lowering conjecture. For all $a\in[1,N]$, the operators $M_{a,0}^{(G)}$ and $M_{a,\pm1}^{(G)}$ act on $\Pi_\lambda^{(G)}$ by the eigenvalue, raising, and lowering formulas stated in the source for types $D_N$, $B_N$, and $C_N$. These formulas would identify the discrete-time Macdonald-operator evolutions at times $\pm1$ as raising and lowering operators for $q$-Whittaker functions; the claim is presented as a conjectural extension of the type-$A$ result and remains open in the supplied text.