Orthogonal Howe duality and dynamical (split) symmetric pairs

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 (so₂₍, Oₘ) -duality and prove that the standard Knizhnik-Zamolodchikov and dynamical operators (both differential and difference) on the so₂₍-side are exchanged with the symmetric pair analogs, for Oₘ GLₘ, on the Oₘ-side.