A new Young wall realization of $B(\lambda)$ and $B(\infty)$

Abstract

Using new combinatorics of Young walls, we give a new construction of the arbitrary level highest weight crystal $B(\lambda)$ for the quantum affine algebras of types $A^{(2)}_{2n}$, $D^{(2)}_{n+1}$, $A^{(2)}_{2n-1}$, $D^{(1)}_n$, $B^{(1)}_n$ and $C^{(1)}_n$. We show that the crystal consisting of reduced Young walls is isomorphic to the crystal $B(\lambda)$. Moreover, we provide a new realization of the crystal $B(\infty)$ in terms of reduced virtual Young walls and reduced extended Young walls.