Three combinatorial models for affine sl(n) crystals, with applications to cylindric plane partitions
Abstract
We define three combinatorial models for \hat{sl(n)} crystals, parametrized by partitions, configurations of beads on an `abacus', and cylindric plane partitions, respectively. These are reducible, but we can identify an irreducible subcrystal corresponding to any dominant integral highest weight. Cylindric plane partitions actually parametrize a basis for the tensor product of an irreducible representation with the space spanned by all partitions. We use this to calculate the partition function for a system of random cylindric plane partitions. We also observe a form of rank level duality. Finally, we use an explicit bijection to relate our work to the Kyoto path model.
Keywords
Cite
@article{arxiv.math/0702062,
title = {Three combinatorial models for affine sl(n) crystals, with applications to cylindric plane partitions},
author = {Peter Tingley},
journal= {arXiv preprint arXiv:math/0702062},
year = {2010}
}
Comments
29 pages, 14 Figures. v2: 5 new references. Minor corrections and clarifications. v3: Section 4.2 corrected