Domain wall six-vertex model with half-turn symmetry

We obtain asymptotic formulas for the partition function of the six-vertex model with domain wall boundary conditions and half-turn symmetry in each of the phase regions. The proof is based on the Izergin--Korepin--Kuperberg determinantal formula for the partition function, its reduction to orthogonal polynomials, and on an asymptotic analysis of the orthogonal polynomials under consideration in the framework of the Riemann--Hilbert approach.