Inverse moment problem for non-Abelian Coxeter double Bruhat cells

TL;DR

This paper addresses the inverse problem for non-Abelian Coxeter double Bruhat cells using matrix Weyl functions, enabling the demonstration of integrability for related nonlinear Coxeter-Toda lattices in matrix groups.

Contribution

It provides a solution to the inverse problem in the non-Abelian setting, extending the theory of Coxeter double Bruhat cells and their integrability properties.

Findings

Solved the inverse problem for non-Abelian Coxeter double Bruhat cells.

Established complete integrability of non-Abelian nonlinear Coxeter-Toda lattices.

Connected matrix Weyl functions to the structure of these cells.

Abstract

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 $GL_n$.