## 84 Citations

Drinfeld J Presentation of Twisted Yangians

- Mathematics
- 2017

We present a quantization of a Lie coideal structure for twisted half-loop algebras of finite-dimensional simple complex Lie algebras. We obtain algebra closure relations of twisted Yangians in…

A family of tridiagonal pairs and related symmetric functions

- Mathematics
- 2006

A family of tridiagonal pairs which appear in the context of quantum integrable systems is studied in detail. The corresponding eigenvalue sequences, eigenspaces and the block tridiagonal structure…

Generalized q-Onsager Algebras and Boundary Affine Toda Field Theories

- Mathematics
- 2009

Generalizations of the q-Onsager algebra are introduced and studied. In one of the simplest case and q = 1, the algebra reduces to the one proposed by Uglov–Ivanov. In the general case and q ≠ 1, an…

Drinfel'd basis of twisted Yangians

- Mathematics
- 2014

We present a quantization of a Lie bi-ideal structure for twisted half-loop algebras of finite dimensional simple complex Lie algebras. We obtain Drinfel'd basis formalism and algebra closure…

FRT presentation of classical Askey–Wilson algebras

- MathematicsLetters in Mathematical Physics
- 2019

Automorphisms of the infinite-dimensional Onsager algebra are introduced. Certain quotients of the Onsager algebra are formulated using a polynomial in these automorphisms. In the simplest case, the…

## References

SHOWING 1-10 OF 52 REFERENCES

Onsager's Algebra and Partially Orthogonal Polynomials

- Mathematics
- 2002

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

- Mathematics
- 1990

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…

Dolan–Grady relations and noncommutative quasi-exactly solvable systems

- Mathematics, Physics
- 2003

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

- Mathematics
- 2001

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

- Mathematics
- 1998

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

- Mathematics
- 2004

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

- Mathematics
- 1994

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…