Braid group action on extended crystals

Abstract

In the paper, we prove that there exists a braid group action on the extended crystal $\hat{B}(\infty )$ of finite type. The extended crystal $\hat{B}(\infty )$ and its braid group action are investigated from the viewpoint of crystal similarity. We then interpret the braid group action on $\hat{B}(\infty )$ in the Hernandez-Leclerc category ${\mathcal{C}}_{\mathfrak{g}}^0$.

32 pages