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

Abstract

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 $\hat{I}»$. We then show that the set $\frac{\infty }{2}\mathrm{LS}(\hat{I}»)$ of semi-infinite LS paths of shape $\hat{I}»$ is isomorphic, as a crystal, to the crystal basis $\mathcal{B}(\hat{I}»)$ of the corresponding level-zero extremal weight module $V(\hat{I}»)$.

29 pages