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Skew Young Diagram Method in Spectral Decomposition of Integrable Lattice Models
被引：0
作者：
A. N. Kirillov
A. Kuniba
T. Nakanishi
机构：
[1] Department of Mathematical Sciences,
[2] University of Tokyo,undefined
[3] Komaba,undefined
[4] Meguro-ku,undefined
[5] Tokyo 153,undefined
[6] Japan,undefined
[7] Institute of Physics,undefined
[8] University of Tokyo,undefined
[9] Komaba,undefined
[10] Meguro-ku,undefined
[11] Tokyo 153,undefined
[12] Japan,undefined
[13] Department of Mathematics,undefined
[14] University of North Carolina,undefined
[15] Chapel Hill,undefined
[16] NC 27599,undefined
[17] USA,undefined
来源：
Communications in Mathematical Physics
|
1997年
/
185卷
关键词：
Lattice Model;
Young Diagram;
Spectral Decomposition;
Integrable Lattice;
Integrable Lattice Model;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
The spectral decomposition of the path space of the vertex model associated
to the vector representation of the quantized affine algebra\documentclass[12pt]{minimal}
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is studied. We give a one-to-one correspondence between
the spin configurations and the semistandard tableaux of skew Young diagrams.
As a result we obtain a formula of the characters for the degeneracy of the
spectrum in terms of skew Schur functions. We conjecture that our
result describes the \documentclass[12pt]{minimal}
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\begin{document}\end{document}-module contents
of the Yangian \documentclass[12pt]{minimal}
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\begin{document}\end{document}-module structures of the level 1 integrable modules of the affine Lie algebra \documentclass[12pt]{minimal}
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\begin{document}\end{document}.
An analogous result is obtained also for a vertex model
associated to the quantized twisted affine
algebra \documentclass[12pt]{minimal}
\usepackage{amsmath}
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\begin{document}\end{document}, where \documentclass[12pt]{minimal}
\usepackage{amsmath}
\usepackage{wasysym}
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\setlength{\oddsidemargin}{-69pt}
\begin{document}\end{document} characters
appear for the degeneracy of the spectrum.
The relations to the spectrum of the Haldane-Shastry and
the Polychronakos
models are also discussed.
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页码：441 / 465
页数：24
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