  We establish a q-version of the Schur-Weyl duality, in which the role of the
symmetric group is played by the Hecke algebra and the role of the enveloping
algebra U(gl(N)) is played by the Reflection Equation algebra, associated with
any skew-invertible Hecke symmetry. Also, in each Reflection Equation algebra
we define analogues of the Schur polynomials and power sums in two forms: as
polynomials in generators of a given Reflection Equation algebra and in terms
of the so-called eigenvalues of the generating matrix $L$, defined by means of
the Cayley-Hamilton identity. It is shown that on any Reflection Equation
algebra there exists a formula, which brings into correlation the Schur
polynomials and power sums by means of the characters of the Hecke algebras in
the spirit of the classical Frobenius formula.
