  We deal with quantum spin chains whose Hamiltonian arises from a
representation of the Temperley-Lieb algebra, and we consider the mean values
of those local operators which are generated by the Temperley-Lieb algebra. We
present two key conjectures which relate these mean values to existing
literature about factorized correlation functions in the XXZ spin chain. The
first conjecture states that the finite volume mean values of the current and
generalized current operators are given by the same simple formulas as in the
case of the XXZ chain. The second conjecture states that the mean values of
products of Temperley-Lieb generators can be factorized: they can expressed as
sums of products of current mean values, such that the coefficients in the
factorization depend neither on the eigenstate in question, nor on the selected
representation of the algebra. The coefficients can be extracted from existing
work on factorized correlation functions in the XXZ model. The conjectures
should hold for all eigenstates that are non-degenerate with respect to the
local charges of the models. We consider concrete representations, where we
check the conjectures: the so-called golden chain, the $Q$-state Potts model,
and the trace representation. We also explain how to derive the generalized
current operators from concrete expressions for the local charges.
