A bijection between type D_n^{(1)} crystals and rigged configurations
Quantum Algebra
2007-05-23 v2 Mathematical Physics
Combinatorics
math.MP
Abstract
Hatayama et al. conjectured fermionic formulas associated with tensor products of U'_q(g)-crystals B^{r,s}. The crystals B^{r,s} correspond to the Kirillov--Reshetikhin modules which are certain finite dimensional U'_q(g)-modules. In this paper we present a combinatorial description of the affine crystals B^{r,1} of type D_n^{(1)}. A statistic preserving bijection between crystal paths for these crystals and rigged configurations is given, thereby proving the fermionic formula in this case. This bijection reflects two different methods to solve lattice models in statistical mechanics: the corner-transfer-matrix method and the Bethe Ansatz.
Keywords
Cite
@article{arxiv.math/0406248,
title = {A bijection between type D_n^{(1)} crystals and rigged configurations},
author = {Anne Schilling},
journal= {arXiv preprint arXiv:math/0406248},
year = {2007}
}
Comments
38 pages; version to appear in J. Algebra