  Inspired by Etingof--Varchenko's dynamical fusion, dynamical $R$-matrix, and
dynamical Weyl group for Lie algebras, we introduce, for split symmetric pairs,
versions of dynamical fusion, dynamical $K$-matrix, and dynamical Weyl group.
We then turn to the study of $(\mathfrak{so}_{2n},O_m)$-duality and prove that
the standard Knizhnik-Zamolodchikov and dynamical operators (both differential
and difference) on the $\mathfrak{so}_{2n}$-side are exchanged with the
symmetric pair analogs, for $O_m\subset GL_m$, on the $O_m$-side.
