A new Young wall realization of B(λ) and B(∞)

Using new combinatorics of Young walls, we give a new construction of the arbitrary level highest weight crystal B(λ) 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(λ). Moreover, we provide a new realization of the crystal B(∞) in terms of reduced virtual Young walls and reduced extended Young walls.