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

Quantum Schur-Weyl duality and q-Frobenius formula related to Reflection Equation algebras