Factorial-type Schur functions, orthogonal rational functions, and discrete dressing chains (Q2814218)

The aim of this paper is to clarify a relationship between orthogonal rational functions and discrete-time integrable systems (discrete dressing chains). It is shown that orthogonal rational functions can be constructed using a multiparameter deformation of the Schur functions, referred to by the authors as factorial-type Schur functions (since they are an extension of the factorial Schur functions). Properties of the factorial-type Schur functions are then used to derive spectral equations for the orthogonal rational functions. The compatibility condition of the spectral equations then leads to a discrete dressing chain, this being a Toda-type discrete-time integrable system describing dressing transformations for orthogonal rational functions.