The tacnode Riemann–Hilbert problem is a 4x4 matrix-valued RH problem that appears in the description of the local behavior of two touching groups of nonintersecting Brownian motions. The same RH problem was also found by Duits
and Geudens to describe a new critical regime in the two-matrix model.
Delvaux gave integral representations for some of the entries of the 4x4 matrix. We complement this work by presenting integral representations for all of the entries.
As a consequence, we give an explicit formula for the Duits–Geudens critical kernel.