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 $\tfrac{\infty}{2}\mathrm{LS}(\lambda)$ 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 $V(\lambda)$.