# On diagonal solutions of the reflection equation

@article{Tsuboi2018OnDS, title={On diagonal solutions of the reflection equation}, author={Zengo Tsuboi}, journal={Journal of Physics A: Mathematical and Theoretical}, year={2018}, volume={52} }

We study solutions of the reflection equation associated with the quantum affine algebra and obtain diagonal K-operators in terms of the Cartan elements of a quotient of Uq(gl(N)). We also consider intertwining relations for these K-operators and find an augmented q-Onsager algebra like symmetry behind them.

## 8 Citations

### Generic triangular solutions of the reflection equation: U q ( s l 2 ̂ ) case

- MathematicsJournal of Physics A: Mathematical and Theoretical
- 2020

We consider intertwining relations of the triangular q-Onsager algebra, and obtain generic triangular boundary K-operators in terms of the Borel subalgebras of U q (sl 2). These K-operators solve the…

### Algebraic Bethe ansatz for Q-operators of the open XXX Heisenberg chain with arbitrary spin

- MathematicsJournal of Physics A: Mathematical and Theoretical
- 2022

In this note we construct Q-operators for the spin s open Heisenberg XXX chain with diagonal boundaries in the framework of the quantum inverse scattering method. Following the algebraic Bethe ansatz…

### A note on q-oscillator realizations of U(gl(M|N)) for Baxter Q-operators

- MathematicsNuclear Physics B
- 2019

### Oscillator realisations associated to the D-type Yangian: Towards the operatorial Q-system of orthogonal spin chains

- Mathematics
- 2020

### Transfer Matrices of Rational Spin Chains via Novel BGG-Type Resolutions

- MathematicsCommunications in Mathematical Physics
- 2023

We obtain BGG-type formulas for transfer matrices of irreducible finite-dimensional representations of the classical Lie algebras $\mathfrak{g}$, whose highest weight is a multiple of a fundamental…

### The alternating presentation of Uq(gl2ˆ) from Freidel-Maillet algebras

- MathematicsNuclear Physics B
- 2021

### Frassek, Rouven Oscillator realisations associated to the D-type Yangian: towards the operatorial Q-system

- Mathematics
- 2021

We present a family of novel Lax operators corresponding to representations of the RTTrealisation of the Yangian associated with D-type Lie algebras. These Lax operators are of oscillator type, i.e.…

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