  The Schur-Weyl states belong to a special class of states with a symmetry
described by two Young and Weyl tableaux. Representation of physical systems in
Hilbert space spanned on these states enables to extract quantum information
hidden in nonlocal degrees of freedom. Such property can be very useful in a
broad range of problems in Quantum Computations, especially in quantum
algorithms constructions, therefore it is very important to know exact form of
these states. Moreover, they allow to reduce significantly the size of
eigenproblem, or in general, diminishing the representation matrix of any
physical quantities, represented in the symmetric or unitary group algebra.
Here we present a new method of Schur-Weyl states construction in a spin chain
system representation. Our approach is based on the fundamental shift operators
out of which one can build Clebsch-Gordan coefficients for the unitary group
U(n) and then derive appropriate Schur-Weyl state probability amplitudes.
