  We propose new explicit form of q-deformed Whittaker functions solving
q-deformed gl(l+1)-Toda chains. In the limit q->1 constructed solutions reduce
to classical class one gl(l+1)-Whittaker functions in the form proposed by
Givental. An important property of the proposed expression for the q-deformed
gl(l+1)-Whittaker function is that it can be represented as a character of C*x
GL(l+1). This provides a q-version of the Shintani-Casselman-Shalika formula
for p-adic Whittaker function. The Shintani-Casselman-Shalika formula is
recovered in the limit q->0 when the q-deformed Whittaker function is reduced
to a character of a finite-dimensional representation of gl(l+1) expressed
through Gelfand-Zetlin bases.
