Asymmetric Twin Representation: the Transfer Matrix Symmetry
The symmetry of the Hamiltonian describing the asymmetric twin model was partially studied in earlier works, and our aim here is to generalize these results for the open transfer matrix. In this spirit we first prove, that the so called boundary quantum algebra provides a symmetry for any generic -...
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| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
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| Date: | 2007 |
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| Format: | Article |
| Language: | English |
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Інститут математики НАН України
2007
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| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/147801 |
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| Cite this: | Asymmetric Twin Representation: the Transfer Matrix Symmetry / A. Doikou // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 36 назв. — англ. |
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Doikou, A. 2019-02-16T08:29:35Z 2019-02-16T08:29:35Z 2007 Asymmetric Twin Representation: the Transfer Matrix Symmetry / A. Doikou // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 36 назв. — англ. 1815-0659 2000 Mathematics Subject Classification: 81R50; 17B37 https://nasplib.isofts.kiev.ua/handle/123456789/147801 The symmetry of the Hamiltonian describing the asymmetric twin model was partially studied in earlier works, and our aim here is to generalize these results for the open transfer matrix. In this spirit we first prove, that the so called boundary quantum algebra provides a symmetry for any generic - independent of the choice of model - open transfer matrix with a trivial left boundary. In addition it is shown that the boundary quantum algebra is the centralizer of the B type Hecke algebra. We then focus on the asymmetric twin representation of the boundary Temperley-Lieb algebra. More precisely, by exploiting exchange relations dictated by the reflection equation we show that the transfer matrix with trivial boundary conditions enjoys the recognized Uq(sl₂) ⊗ Ui(sl₂) symmetry. When a non-diagonal boundary is implemented the symmetry as expected is reduced, however again certain familiar boundary non-local charges turn out to commute with the corresponding transfer matrix. This paper is a contribution to the Vadim Kuznetsov Memorial Issue “Integrable Systems and Related Topics”. I am thankful to P.P. Martin for useful discussions. This work is supported by INFN, and the European Network ‘EUCLID’; ‘Integrable models and applications: from strings to condensed matter’, contract number HPRN–CT–2002–00325. en Інститут математики НАН України Symmetry, Integrability and Geometry: Methods and Applications Asymmetric Twin Representation: the Transfer Matrix Symmetry Article published earlier |
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Digital Library of Periodicals of National Academy of Sciences of Ukraine |
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| title |
Asymmetric Twin Representation: the Transfer Matrix Symmetry |
| spellingShingle |
Asymmetric Twin Representation: the Transfer Matrix Symmetry Doikou, A. |
| title_short |
Asymmetric Twin Representation: the Transfer Matrix Symmetry |
| title_full |
Asymmetric Twin Representation: the Transfer Matrix Symmetry |
| title_fullStr |
Asymmetric Twin Representation: the Transfer Matrix Symmetry |
| title_full_unstemmed |
Asymmetric Twin Representation: the Transfer Matrix Symmetry |
| title_sort |
asymmetric twin representation: the transfer matrix symmetry |
| author |
Doikou, A. |
| author_facet |
Doikou, A. |
| publishDate |
2007 |
| language |
English |
| container_title |
Symmetry, Integrability and Geometry: Methods and Applications |
| publisher |
Інститут математики НАН України |
| format |
Article |
| description |
The symmetry of the Hamiltonian describing the asymmetric twin model was partially studied in earlier works, and our aim here is to generalize these results for the open transfer matrix. In this spirit we first prove, that the so called boundary quantum algebra provides a symmetry for any generic - independent of the choice of model - open transfer matrix with a trivial left boundary. In addition it is shown that the boundary quantum algebra is the centralizer of the B type Hecke algebra. We then focus on the asymmetric twin representation of the boundary Temperley-Lieb algebra. More precisely, by exploiting exchange relations dictated by the reflection equation we show that the transfer matrix with trivial boundary conditions enjoys the recognized Uq(sl₂) ⊗ Ui(sl₂) symmetry. When a non-diagonal boundary is implemented the symmetry as expected is reduced, however again certain familiar boundary non-local charges turn out to commute with the corresponding transfer matrix.
|
| issn |
1815-0659 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/147801 |
| citation_txt |
Asymmetric Twin Representation: the Transfer Matrix Symmetry / A. Doikou // Symmetry, Integrability and Geometry: Methods and Applications. — 2007. — Т. 3. — Бібліогр.: 36 назв. — англ. |
| work_keys_str_mv |
AT doikoua asymmetrictwinrepresentationthetransfermatrixsymmetry |
| first_indexed |
2025-11-30T13:00:00Z |
| last_indexed |
2025-11-30T13:00:00Z |
| _version_ |
1850857690090176512 |