Folded and contracted solutions of coupled classical dynamical Yang–Baxter and reflection equations

In this paper we give a concrete recipe how to construct triples of algebra-valued meromorphic functions on complex vector space satisfying three coupled classical dynamical Yang–Baxter equations and an associated reflection equation. Such provide the local factors consistent system first order differential operators a, generalising asymptotic boundary Knizhnik–Zamolodchikov–Bernard (KZB) equations. The involves folding contracting a-invariant θ-twisted symmetric r-matrices along involutive automorphism θ. case universal enveloping algebra simple Lie g determine subclass Schiffmann’s which are θ-twisted. starts with section highlighting connections between (boundary) KZB equations, representation theory semisimple groups, integrable quantum field theories.