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 $A_{2n}^{(2)}$, $D_{n+1}^{(2)}$, $A_{2n-1}^{(2)}$, $D_n^{(1)}$, $B_n^{(1)}$ and $C_n^{(1)}$. 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.