A bijection between type Dn(1) crystals and rigged configurations
Abstract
Hatayama et al. conjectured fermionic formulas associated with tensor products of U'q(g)-crystals Br,s. The crystals Br,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 Br,1 of type Dn(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.
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