  We identify q-deformed gl(l+1)-Whittaker functions with a specialization of
Macdonald polynomials. This provides a representation of q-deformed
gl(l+1)-Whittaker functions in terms of Demazure characters of affine Lie
algebra \hat{gl(l+1)}. We also define a system of dual Hamiltonians for
q-deformed gl(l+1)-Toda chains and give a new integral representation for
q-deformed gl(l+1)-Whittaker functions. Finally an expression of q-deformed
gl(l+1)-Whittaker function as a matrix element of a quantum torus algebra is
derived.
