An integrable structure related with tridiagonal algebras

@article{Baseilhac2005AnIS,
  title={An integrable structure related with tridiagonal algebras},
  author={Pascal Baseilhac},
  journal={Nuclear Physics},
  year={2005},
  volume={705},
  pages={605-619}
}
  • P. Baseilhac
  • Published 14 August 2004
  • Mathematics
  • Nuclear Physics
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References

SHOWING 1-10 OF 52 REFERENCES
Onsager's Algebra and Partially Orthogonal Polynomials
The energy eigenvalues of the superintegrable chiral Potts model are determined by the zeros of special polynomials which define finite representations of Onsager's algebra. The polynomials
Onsager's algebra and superintegrability
The author considers the irreducible representations of the Onsager algebra, and shows that for a finite system, possessing such an algebra leads to an Ising-like structure in the spectra of
Deformed Dolan-Grady relations in quantum integrable models
Dolan–Grady relations and noncommutative quasi-exactly solvable systems
We investigate a U(1) gauge invariant quantum mechanical system on a 2D noncommutative space with coordinates generating a generalized deformed oscillator algebra. The Hamiltonian is taken as a
Quantum Group Symmetry in sine-Gordon and Affine Toda Field Theories on the Half-Line
Abstract: We consider the sine-Gordon and affine Toda field theories on the half-line with classically integrable boundary conditions, and show that in the quantum theory a remnant survives of the
Integrable Structure of Conformal Field Theory III. The Yang–Baxter Relation
Abstract:In this paper we fill some gaps in the arguments of our previous papers [1,2]. In particular, we give a proof that the L operators of Conformal Field Theory indeed satisfy the defining
Boundary quantum group generators from the open transfer matrix
We present a systematic way of constructing boundary quantum group generators associated to non-diagonal solutions of the reflection equation for the XXZ model. This is achieved by studying the
A guide to quantum groups
Introduction 1. Poisson-Lie groups and Lie bialgebras 2. Coboundary Poisson-Lie groups and the classical Yang-Baxter equation 3. Solutions of the classical Yang-Baxter equation 4. Quasitriangular
...
1
2
3
4
5
...