Monomial Crystals and Partition Crystals

Abstract

Recently Fayers introduced a large family of combinatorial realizations of the fundamental crystal B(Λ₀) for sln, where the vertices are indexed by certain partitions. He showed that special cases of this construction agree with the Misra-Miwa realization and with Berg's ladder crystal. Here we show that another special case is naturally isomorphic to a realization using Nakajima's monomial crystal.