Semi-infinite Lakshmibai--Seshadri paths and level-zero extremal weight modules over twisted quantum affine algebras

In this paper, we study level-zero extremal weight modules over twisted quantum affine algebras. To this end, we introduce semi-infinite Lakshmibai–Seshadri paths associated with a level-zero dominant integral weight $\lambda$. We then show that the set $\frac{\mathrm{\infty }}{2}\mathrm{L}\mathrm{S}(\lambda )$ of semi-infinite LS paths of shape $\lambda$ is isomorphic, as a crystal, to the crystal basis $\mathcal{B}(\lambda )$ of the corresponding level-zero extremal weight module $V(\lambda )$.