  The low-energy excitations and $\beta$ decays of odd-A nuclei are studied
within the interacting boson-fermion model (IBFM), based on the Gogny-D1M
nuclear energy density functional (EDF). The constrained
Hartree-Fock-Bogoliubov (HFB) approximation is employed to compute potential
energy surfaces in terms of triaxial quadrupole degrees of freedom for
even-even Xe and Ba nuclei in the mass $A\approx 130$ region. The mean field
approximation also provides spherical single-particle energies and occupation
probabilities for the neighboring odd-A nuclei. Those quantities represent a
microscopic input for spectroscopic calculations in odd-A Xe and Ba, Cs and La
isotopes. The Gamow-Teller (GT) and Fermi (F) transition matrix elements,
needed to compute $\beta$-decay $\log{ft}$ values are obtained without any
phenomenological fitting. It is shown that both the low-lying states and
$\beta$ decays of the studied odd-A systems are described reasonably well
within the employed theoretical framework.
