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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| Дата: | 2006 |
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| Автор: | |
| Формат: | Стаття |
| Мова: | English |
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Інститут математики НАН України
2006
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| Назва видання: | Symmetry, Integrability and Geometry: Methods and Applications |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/146446 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Цитувати: | 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. |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
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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 |