  Integrable open quantum spin-chain transfer matrices constructed from
trigonometric R-matrices associated to affine Lie algebras $\hat g$, and from
certain K-matrices (reflection matrices) depending on a discrete parameter p,
were recently considered in arXiv:1802.04864 and arXiv:1805.10144. It was shown
there that these transfer matrices have quantum group symmetry corresponding to
removing the p-th node from the $\hat g$ Dynkin diagram. Here we determine the
spectrum of these transfer matrices by using analytical Bethe ansatz, and we
determine the dependence of the corresponding Bethe equations on p. We propose
formulas for the Dynkin labels of the Bethe states in terms of the numbers of
Bethe roots of each type.We also briefly study how duality transformations are
implemented on the Bethe ansatz solutions.
