A New Young Wall Realization of B ( λ ) and B ( ∞ )

Abstract

Using new combinatorics of Young walls, we give a new construction of the arbitrary level highest weight crystal [Formula: see text] for the quantum affine algebras of types [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text], [Formula: see text] and [Formula: see text]. We show that the crystal consisting of reduced Young walls is isomorphic to the crystal [Formula: see text]. Moreover, we provide a new realization of the crystal [Formula: see text] in terms of reduced virtual Young walls and reduced extended Young walls.