In the paper, we prove that there exists a braid group action on extended crystal Bˆ(∞) of finite type. The and its are investigated from viewpoint similarity. We then interpret in Hernandez-Leclerc category Cg0.

Let ? be a simple undirected graph on finite vertex set and let A its adjacency matrix. Then is singular if singular. The problem of characterizing graphs easy to state but very difficult resolve in any generality. In this paper we investigate the singularity for which dihedral group acts transitively vertices as automorphisms.