  We study the equation of state of neutron-star matter including the effects
of isovector-vector coupling in quark matter. We employ the relativistic
mean-field theory with an extended TM1 parameter set to describe hadronic
matter and the SU(3) Nambu-Jona-Lasinio model with isovector-vector and
hypercharge-vector couplings to describe the quark matter. The deconfinement
hadron-quark phase transition is constructed under Gibbs phase equilibrium
conditions. It is found that the isovector-vector and hypercharge-vector
couplings in quark matter enhance the symmetry energy and hypercharge symmetry
energy in neutron-star matter.
