  We pursue the group theoretical method to study Isgur-Wise functions. We
apply the general formalism, formerly applied to the baryon case j^P = 0^+ (for
\Lambda_b -> \Lambda_c \ell \nu), to mesons with j^P = 1/2^-, i.e.
$\overline{B} -> D(D^{(*)})\ell\nu. In this case, more involved from the
angular momentum point of view, only the principal series of unitary
representations of the Lorentz group contribute. We obtain an integral
representation for the IW function xi(w) with a positive measure, recover the
bounds for the slope and the curvature of xi(w) obtained from the
Bjorken-Uraltsev sum rule method, and get new bounds for higher derivatives. We
demonstrate also that if the lower bound for the slope is saturated, the
measure is a delta-function, and xi(w) is given by an explicit elementary
function. Inverting the integral formula, we obtain the measure in terms of the
IW function, allowing to formulate criteria to decide if a given ansatz for the
Isgur-Wise function is compatible or not with the sum rule constraints.
Moreover, we have obtained an upper bound on the IW function valid for any
value of w. We compare these theoretical constraints to a number of forms for
\xi(w) proposed in the literature. The "dipole" function \xi(w) =
(2/(w+1))^(2c) satisfies all constraints for c \geq 3/4, while the QCD Sum Rule
result including condensates does not satisfy them. Special care is devoted to
the Bakamjian-Thomas relativistic quark model in the heavy quark limit and to
the description of the Lorentz group representation that underlies this model.
Consistently, the IW function satisfies all Lorentz group criteria for any
explicit form of the meson Hamiltonian at rest.
