  We use power sums plethysm operators to introduce H functions which
interpolate between the Weyl characters and the Hall-Littlewood functions Q'
corresponding to classical Lie groups. The coefficients of these functions on
the basis of Weyl characters are parabolic Kazhdan-Lusztig polynomials and
thus, are nonnegative. We prove that they can be regarded as quantizations of
branching coefficients obtained by restriction to certain Levi subgroups. The H
functions associated to linear groups coincide with the polynomials introduced
by Lascoux Leclerc and Thibon (LLT polynomials).
