Modified Nakajima monomials and the crystal [formula omitted

Abstract

In this paper, we give a new realization of the crystal B ( ∞ ) using modified Nakajima monomials. For the quantum affine algebras of type A n ( 1 ) , we give an explicit characterization of the monomials in B ( ∞ ) , and construct a natural crystal isomorphism between monomial realization and path realization. As a corollary, we obtain a new realization of the crystal B ( ∞ ) for the quantum classical algebras of type A n .