FACES OF RELATIVISTIC TODA CHAIN

We demonstrate that the generalization of the relativistic Toda chain (RTC) is a special reduction of two-dimensional Toda lattice hierarchy (2DTL). This reduction implies that the RTC is gauge equivalent to th e discrete AKNS hierarchy and, which is the same, to the two-component Volterra hierarchy while its forced (semi-infinite) variant is descri bed by the unitary matrix integral. The integrable properties of the R TC hierarchy are revealed in different frameworks of the Lax represent ation, orthogonal polynomial systems, and tau-function approach. Relat ivistic Toda molecule hierarchy is also considered, along with the for ced RTC. Some applications to biorthogonal polynomial systems are disc ussed.