×

Junction type representations of the Temperley-Lieb algebra and associated symmetries. (English) Zbl 1217.81115

Summary: 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.

MSC:

81R50 Quantum groups and related algebraic methods applied to problems in quantum theory
17B37 Quantum groups (quantized enveloping algebras) and related deformations
17B80 Applications of Lie algebras and superalgebras to integrable systems
81R15 Operator algebra methods applied to problems in quantum theory
81R12 Groups and algebras in quantum theory and relations with integrable systems
PDFBibTeX XMLCite
Full Text: DOI arXiv EuDML