Monomial Crystals and Partition Crystals

• Main Author: Tingley, Peter William (Contributor)
• Other Authors: Massachusetts Institute of Technology. Department of Mathematics (Contributor)
• Format: Article
• Language: English
• Published: National Academy of Sciences of Ukraine (SIGMA (Symmetry, Integrability, and Geometry: Methods and Application)), 2014-09-16T19:28:15Z.
• Subjects: Article
• Online Access: Get fulltext

Recently Fayers introduced a large family of combinatorial realizations of the fundamental crystal B(Λ[subscript 0]) for [^ over sl][subscript 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.
National Science Foundation (U.S.) (Grant DMS-0902649)