1,335 research outputs found
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 ,
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
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