Monomial Crystals and Partition Crystals

Abstract

Recently Fayers introduced a large family of combinatorial realizations of the fundamental crystal for affine sl(n), 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.

4 figures; v2: minor edits for clarity; v3: published version

References in corpus (2)

• Three combinatorial models for affine sl(n) crystals, with applications to cylindric plane partitions
• Partition models for the crystal of the basic $U_q({\widehat{\mathfrak{sl}}}_n)$-module

Cited by in corpus (2)

• Combinatorial realizations of crystals via torus actions on quiver varieties
• Partition models for the crystal of the basic $U_q({\widehat{\mathfrak{sl}}}_n)$-module