M. I. Gekhtman
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Methods Funct. Anal. Topology 22 (2016), no. 2, 117-136
We solve the inverse problem for non-Abelian Coxeter double Bruhat cells in terms of the matrix Weyl functions. This result can be used to establish complete integrability of the non-Abelian version of nonlinear Coxeter-Toda lattices in $GL_n$.