<p>Inspired by Etingof–Varchenko’s dynamical Weyl group for Lie algebras and Reshetikhin–Stokman’s boundary fusion operators for split symmetric pairs, we introduce a dynamical Weyl group for split symmetric pairs. We then turn to the study of <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\((\mathfrak {so}_{2n},\textrm{O}_m)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <msub> <mi mathvariant="fraktur">so</mi> <mrow> <mn>2</mn> <mi>n</mi> </mrow> </msub> <mo>,</mo> <msub> <mtext>O</mtext> <mi>m</mi> </msub> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>-duality and prove that the standard Knizhnik–Zamolodchikov and dynamical operators (both differential and difference) on the <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\mathfrak {so}_{2n}\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mi mathvariant="fraktur">so</mi> <mrow> <mn>2</mn> <mi>n</mi> </mrow> </msub> </math></EquationSource> </InlineEquation>-side are exchanged with the symmetric pair analogs, for <InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(\textrm{O}_m\subset \textrm{GL}_m\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msub> <mtext>O</mtext> <mi>m</mi> </msub> <mo>⊂</mo> <msub> <mtext>GL</mtext> <mi>m</mi> </msub> </mrow> </math></EquationSource> </InlineEquation>, on the <InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(\textrm{O}_m\)</EquationSource> <EquationSource Format="MATHML"><math> <msub> <mtext>O</mtext> <mi>m</mi> </msub> </math></EquationSource> </InlineEquation>-side.</p>