Crystal B(lambda) as a subset of crystal B(infinity) expressed as tableaux for A(n), type

Abstract

The crystal B (infinity) circle times T-lambda is known to contain a copy of the irreducible highest weight crystal B(lambda) as a sub-crystal. By explicitly identifying the elements belonging to the mentioned sub-crystal, we present two realizations of B(lambda) that are based on two realizations of B(infinity), for the special linear Lie algebra type. The first description of B(A) is based on our new realization of B(infinity) as the set of all marginally large reverse tableaux and the second is based on a previous realization of B(infinity) as the set of all marginally large tableaux. We further present two new Nakajima monomial realizations of B(lambda) that correspond naturally to our reverse. tableau and tableau realizations