  We present a theory of interacting valence holes in a gate-defined
one-dimensional quantum channel in a single layer of a transition metal
dichalcogenide material WSe$_2$. Based on a microscopic atomistic tight-binding
model and Hartree-Fock and exact configuration-interaction tools we demonstrate
the possibility of symmetry-broken valley polarized states for strongly
interacting holes. The interplay between interactions, perpendicular magnetic
field, and the lateral confinement asymmetry together with the strong Rashba
spin-orbit coupling present in WSe$_2$ material is analyzed, and its impact on
valley polarization is discussed. For weaker interactions, an investigation of
the pair correlation function reveals a valley-antiferromagnetic phase. For low
hole densities, a formation of a zigzag Wigner crystal phase is predicted. The
impact of various hole liquid phases on transport in a high mobility quasi-one
dimensional channel is discussed.
