Simplicity and similarity of Kirillov-Reshetikhin crystals

We show that the Kirillov-Reshetikhin crystal B^{r,s} for nonexceptional affine types is simple and have the similarity property. As a corollary of the first fact we can derive that the tensor product of KR crystals is connected. Variations of the second property are also given.Comment: 11 pages. arXiv admin note: text overlap with arXiv:0810.506

Excitation Spectra of Spin Models constructed from Quantized Affine Algebras of type Bn(1)B_n^{(1)}, Dn(1)D_n^{(1)}

The energy and momentum spectrum of the spin models constructed from the vector representation of the quantized affine algebras of type \B and \D are computed using the approach of Davies et al. \cite{DFJMN92}. The results are for the anti-ferromagnetic (massive) regime, and they agree with the mass spectrum found from the factorized S--matrix theory by Ogievetsky et al. \cite{ORW87}. The other new result is the explicit realization of the fusion construction for the quantized affine algebras of type \B and \D.}Comment: Plain TeX --- 178k including 3 eps files. 1. For correct cross-references, run twice (as with LaTeX). 2. The FIGURES for this paper are at the end of this file. They must split off and saved with names fig1.eps, fig2.eps, fig3.eps The standard macros package epsf.tex is also require

Existence of Kirillov-Reshetikhin crystals for nonexceptional types

Using the methods of Kang et al. and recent results on the characters of Kirillov-Reshetikhin modules by Nakajima and Hernandez, the existence of Kirillov-Reshetikhin crystals B^{r,s} is established for all nonexceptional affine types. We also prove that the crystals B^{r,s} of type B_n^{(1)}, D_n^{(1)}, and A_{2n-1}^{(2)} are isomorphic to recently constructed combinatorial crystals for r not a spin node.Comment: 23 pages; version that appeared in Representation Theory and erratum adde

Affine crystal structure on rigged configurations of type D_n^(1)

Extending the work arXiv:math/0508107, we introduce the affine crystal action on rigged configurations which is isomorphic to the Kirillov-Reshetikhin crystal B^{r,s} of type D_n^(1) for any r,s. We also introduce a representation of B^{r,s} (r not equal to n-1,n) in terms of tableaux of rectangular shape r x s, which we coin Kirillov-Reshetikhin tableaux (using a non-trivial analogue of the type A column splitting procedure) to construct a bijection between elements of a tensor product of Kirillov-Reshetikhin crystals and rigged configurations.Comment: 26 pages, 3 figures. (v3) corrections in the proof reading. (v2) 26 pages; examples added; introduction revised; final version. (v1) 24 page