  For a reductive Lie algebra g, its nilpotent element f and its faithful
finite dimensional representation, we construct a Lax operator L(z) with
coefficients in the quantum finite W-algebra W(g,f). We show that for the
classical linear Lie algebras gl_N, sl_N, so_N and sp_N, the operator L(z)
satisfies a generalized Yangian identity. The operator L(z) is a quantum finite
analogue of the operator of generalized Adler type which we recently introduced
in the classical affine setup. As in the latter case, L(z) is obtained as a
generalized quasideterminant.
