On diagonal solutions of the reflection equation

  title={On diagonal solutions of the reflection equation},
  author={Zengo Tsuboi},
  journal={Journal of Physics A: Mathematical and Theoretical},
  • Z. Tsuboi
  • Published 26 November 2018
  • Mathematics
  • Journal of Physics A: Mathematical and Theoretical
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. 

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

  • Z. Tsuboi
  • Mathematics
    Journal 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

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

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

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

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.



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

Universal L operator and invariants of the quantum supergroup Uq(gl(m/n))

A spectral parameter‐dependent solution of the graded Yang–Baxter equation is obtained, which is universal in the sense that it lives in Uq(gl(m/n))⊗End(V) with V the vector module of Uq(gl(m/n)).

A q-analogue of U(g[(N+1)), Hecke algebra, and the Yang-Baxter equation

We study for g=g[(N+1) the structure and representations of the algebra Ŭ(g), a q-analogue of the universal enveloping algebra U(g). Applying the result, we construct trigonometric solutions of the

Q-operators for the open Heisenberg spin chain

Exercises with the universal R-matrix

Using the formula for the universal R-matrix proposed by Khoroshkin and Tolstoy, we give a detailed derivation of L-operators for the quantum groups associated with the generalized Cartan matrices

Q-analogues of Clifford and Weyl algebras-spinor and oscillator representations of quantum enveloping algebras

We introduceq-analogues of Clifford and Weyl algebras. Using these, we construct spinor and oscillator representations of quantum enveloping algebras of typeAN−1,BN,CN,DN andAN−1(1). Also we discuss

Boundary conditions for integrable quantum systems

A new class of boundary conditions is described for quantum systems integrable by means of the quantum inverse scattering (R-matrix) method. The method proposed allows the author to treat open

A Holstein-Primakoff and a Dyson realization for the quantum algebra

The known Holstein-Primakoff and Dyson realizations of the Lie algebra , in terms of Bose operators are generalized to the class of the quantum algebras for any n. It is shown how the elements of can