  We modify and give complete proofs for the results of
Etingof-Schiffmann-Varchenko on traces of intertwiners of untwisted quantum
affine algebras in the opposite coproduct and the standard grading. More
precisely, we show that certain normalized generalized traces for
$U_q(\hat{\mathfrak{g}})$ solve four commuting systems of q-difference
equations: the Macdonald-Ruijsenaars, dual Macdonald-Ruijsenaars, q-KZB, and
dual q-KZB equations. In addition, we show a symmetry property for these
renormalized trace functions. Our modifications are motivated by their
appearance in recent work of the author.
