  Every two variable rational inner function on the bidisk has a special
representation called a transfer function realization. It is well known and
related to important ideas in operator theory that this does not extend to
three or more variables on the polydisk. We study the class of rational inner
functions on the polydisk which do possess a transfer function realization (the
Schur-Agler class) and investigate minimality in their representations.
Schur-Agler class rational inner functions in three or more variables cannot be
represented in a way that is as minimal as two variables might suggest.
