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Junction Type Representations of the Temperley-Lieb Algebra and Associated Symmetries
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2010, том 6
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Junction Type Representations of the Temperley-Lieb Algebra and Associated Symmetries
Інший ID:
2010 Mathematics Subject Classification: 81R50; 17B37; 17B80
DOI:10.3842/SIGMA.2010.089
DOI:10.3842/SIGMA.2010.089
Посилання:
Junction Type Representations of the Temperley-Lieb Algebra and Associated Symmetries / A. Doikou, N. Karaiskos // Symmetry, Integrability and Geometry: Methods and Applications. — 2010. — Т. 6. — Бібліогр.: 24 назв. — англ.
Підтримка:
This paper is a contribution to the Proceedings of the International Workshop “Recent Advances in Quantum Integrable Systems”. The full collection is available at http://www.emis.de/journals/SIGMA/RAQIS2010.html.
NK acknowledges financial support provided by the Research Committee of the University of Patras via a K.Karatheodori fellowship under contract number C.915, and partial support by the LLP/Erasmus Placements 2009-2010 program with contract 0099/2009. He would also like to thank the CPhT of Ecole Polytechnique for kind hospitality and partial support by the ERC Advanced Grant 226371, the ITN programme PITN- GA-2009-237920 and the IFCPAR CEFIPRA programme 4104-2 during the completion of this work.
Дата:
2010
Переглядів:
612
Завантажень:
264
Анотація:
Inspired by earlier works on representations of the Temperley-Lieb algebra we introduce a novel family of representations of the algebra. This may be seen as a generalization of the so called asymmetric twin representation. The underlying symmetry algebra is also examined and it is shown that in addition to certain obvious exact quantum symmetries non trivial quantum algebraic realizations that exactly commute with the representation also exist. Non trivial representations of the boundary Temperley-Lieb algebra as well as the related residual symmetries are also discussed. The corresponding novel R and K matrices solutions of the Yang-Baxter and reflection equations are identified, the relevant quantum spin chain is also constructed and its exact symmetries are studied.
