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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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2006 |
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| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2006
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/146446 |
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| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | 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| _version_ | 1862656400328491008 |
|---|---|
| author | Deguchi, T. |
| author_facet | Deguchi, T. |
| 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. |
| collection | DSpace DC |
| container_title | Symmetry, Integrability and Geometry: Methods and Applications |
| 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.
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| first_indexed | 2025-12-02T04:56:40Z |
| format | Article |
| fulltext | |
| id | nasplib_isofts_kiev_ua-123456789-146446 |
| institution | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| issn | 1815-0659 |
| language | English |
| last_indexed | 2025-12-02T04:56:40Z |
| publishDate | 2006 |
| publisher | Інститут математики НАН України |
| record_format | dspace |
| spelling | Deguchi, T. 2019-02-09T17:19:56Z 2019-02-09T17:19:56Z 2006 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 https://nasplib.isofts.kiev.ua/handle/123456789/146446 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. The author would like to thank K. Fabricius and B.M. McCoy for useful discussions. He would also like to thank the organizers for their kind invitation to the Sixth International Conference “Symmetry in Nonlinear Mathematical Physics”, June 20–26, 2005, Institute of Mathematics, Kyiv, Ukraine. He is grateful to many participants of the conference for useful comments and discussions. This work is partially supported by the Grant-in-Aid (No. 17540351). en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications On the Degenerate Multiplicity of the sl₂ Loop Algebra for the 6V Transfer Matrix at Roots of Unity Article published earlier |
| spellingShingle | On the Degenerate Multiplicity of the sl₂ Loop Algebra for the 6V Transfer Matrix at Roots of Unity Deguchi, T. |
| title | 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_short | 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 |
| url | https://nasplib.isofts.kiev.ua/handle/123456789/146446 |
| work_keys_str_mv | AT deguchit onthedegeneratemultiplicityofthesl2loopalgebraforthe6vtransfermatrixatrootsofunity |