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On the Degenerate Multiplicity of the sl₂ Loop Algebra for the 6V Transfer Matrix at Roots of Unity

On the Degenerate Multiplicity of the sl₂ Loop Algebra for the 6V Transfer Matrix at Roots of Unity

We review the main result of cond-mat/0503564. The Hamiltonian of the XXZ spin chain and the transfer matrix of the six-vertex model has the sl₂ loop algebra symmetry if the q parameter is given by a root of unity, q₀2N = 1, for an integer N. We discuss the dimensions of the degenerate eigenspace ge...

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Main Author: Deguchi, T.
Format: Article
Language:English
Published: Інститут математики НАН України 2006
Series:Symmetry, Integrability and Geometry: Methods and Applications
Online Access:http://dspace.nbuv.gov.ua/handle/123456789/146446
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spelling irk-123456789-1464462019-02-11T01:23:28Z On the Degenerate Multiplicity of the sl₂ Loop Algebra for the 6V Transfer Matrix at Roots of Unity Deguchi, T. We review the main result of cond-mat/0503564. The Hamiltonian of the XXZ spin chain and the transfer matrix of the six-vertex model has the sl₂ loop algebra symmetry if the q parameter is given by a root of unity, q₀2N = 1, for an integer N. We discuss the dimensions of the degenerate eigenspace generated by a regular Bethe state in some sectors, rigorously as follows: We show that every regular Bethe ansatz eigenvector in the sectors is a highest weight vector and derive the highest weight dk±, which leads to evaluation parameters aj. If the evaluation parameters are distinct, we obtain the dimensions of the highest weight representation generated by the regular Bethe state. 2006 Article On the Degenerate Multiplicity of the sl₂ Loop Algebra for the 6V Transfer Matrix at Roots of Unity / T. Deguchi // Symmetry, Integrability and Geometry: Methods and Applications. — 2006. — Т. 2. — Бібліогр.: 30 назв. — англ. 1815-0659 2000 Mathematics Subject Classification: 81R10; 81R12; 81R50; 81V70 http://dspace.nbuv.gov.ua/handle/123456789/146446 en Symmetry, Integrability and Geometry: Methods and Applications Інститут математики НАН України
institution Digital Library of Periodicals of National Academy of Sciences of Ukraine
collection DSpace DC
language English
description We review the main result of cond-mat/0503564. The Hamiltonian of the XXZ spin chain and the transfer matrix of the six-vertex model has the sl₂ loop algebra symmetry if the q parameter is given by a root of unity, q₀2N = 1, for an integer N. We discuss the dimensions of the degenerate eigenspace generated by a regular Bethe state in some sectors, rigorously as follows: We show that every regular Bethe ansatz eigenvector in the sectors is a highest weight vector and derive the highest weight dk±, which leads to evaluation parameters aj. If the evaluation parameters are distinct, we obtain the dimensions of the highest weight representation generated by the regular Bethe state.
format Article
author Deguchi, T.
spellingShingle Deguchi, T.
On the Degenerate Multiplicity of the sl₂ Loop Algebra for the 6V Transfer Matrix at Roots of Unity
Symmetry, Integrability and Geometry: Methods and Applications
author_facet Deguchi, T.
author_sort Deguchi, T.
title On the Degenerate Multiplicity of the sl₂ Loop Algebra for the 6V Transfer Matrix at Roots of Unity
title_short On the Degenerate Multiplicity of the sl₂ Loop Algebra for the 6V Transfer Matrix at Roots of Unity
title_full On the Degenerate Multiplicity of the sl₂ Loop Algebra for the 6V Transfer Matrix at Roots of Unity
title_fullStr On the Degenerate Multiplicity of the sl₂ Loop Algebra for the 6V Transfer Matrix at Roots of Unity
title_full_unstemmed On the Degenerate Multiplicity of the sl₂ Loop Algebra for the 6V Transfer Matrix at Roots of Unity
title_sort on the degenerate multiplicity of the sl₂ loop algebra for the 6v transfer matrix at roots of unity
publisher Інститут математики НАН України
publishDate 2006
url http://dspace.nbuv.gov.ua/handle/123456789/146446
citation_txt On the Degenerate Multiplicity of the sl₂ Loop Algebra for the 6V Transfer Matrix at Roots of Unity / T. Deguchi // Symmetry, Integrability and Geometry: Methods and Applications. — 2006. — Т. 2. — Бібліогр.: 30 назв. — англ.
series Symmetry, Integrability and Geometry: Methods and Applications
work_keys_str_mv AT deguchit onthedegeneratemultiplicityofthesl2loopalgebraforthe6vtransfermatrixatrootsofunity
first_indexed 2023-05-20T17:24:24Z
last_indexed 2023-05-20T17:24:24Z
_version_ 1796153219148152832

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