Generalized Young Walls for Classical Lie Algebras

Abstract

In this paper, we introduce an new combinatorial model, which we call generalized Young walls for classical Lie algebras, and we give two realizations of the crystal B(∞) over classical Lie algebras using generalized Young walls. Also, we construct natural crystal isomorphisms between generalized Young wall realizations and other realizations, for example, monomial realization, polyhedral realization and tableau realization. Moreover, as applications, we obtain a crystal isomorphism between two different polyhedral realizations of B(∞).