Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)


SIGMA 6 (2010), 035, 8 pages      arXiv:0909.2242      http://dx.doi.org/10.3842/SIGMA.2010.035

Monomial Crystals and Partition Crystals

Peter Tingley
Department of Mathematics, Massachusetts Institute of Technology, 77 Massachusetts Avenue, Cambridge, MA 02139, USA

Received February 10, 2010, in final form April 12, 2010; Published online April 21, 2010

Abstract
Recently Fayers introduced a large family of combinatorial realizations of the fundamental crystal B0) 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.

Key words: crystal basis; partition; affine Kac-Moody algebra.

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