  We call a multivariable polynomial an Agler denominator if it is the
denominator of a rational inner function in the Schur-Agler class, an important
subclass of the bounded analytic functions on the polydisk. We give a necessary
and sufficient condition for a multi-affine, symmetric, and stable polynomial
to be an Agler denominator and prove several consequences. We also sharpen a
result due to Kummert related to three variable, multi-affine, stable
polynomials.
