Junction type representations of the Temperley-Lieb algebra and associated symmetries

Abstract

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 symmetry is studied.

19 pages, LaTex. Published in Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

References in corpus (10)

• Associative-algebraic approach to logarithmic conformal field theories
• The two-boundary Temperley-Lieb algebra
• Integrable Boundary Conditions and W-Extended Fusion in the Logarithmic Minimal Models LM(1,p)
• From affine Hecke algebras to boundary symmetries
• Baxterized Solutions of Reflection Equation and Integrable Chain Models
• On quantum group symmetry and Bethe ansatz for the asymmetric twin spin chain with integrable boundary
• Quantum symmetry algebras of spin systems related to Temperley-Lieb R-matrices
• Baxterization of solutions to reflection equation with Hecke R-matrix
• Asymmetric Twin Representation: the Transfer Matrix Symmetry
• Spectral equivalences and symmetry breaking in integrable SU_q(N) spin chains with boundaries