Solutions to the Yang-Baxter equations with $os{p}_q(1|2)$ symmetry: Lax operators

Abstract

We find a new $4\times 4$ solution to the $os{p}_q(1|2)$-invariant Yang-Baxter equation with simple dependence on the spectral parameter and propose $2\times 2$ matrix expressions for the corresponding Lax operator. The general inhomogeneous universal spectral-parameter dependent $R$-matrix is derived. It is proven, that there are two independent solutions to the homogeneous $os{p}_q(1|2)$-invariant YBE, defined on the fundamental three dimensional representations. One of them is the particular case of the universal matrix, while the second one does not admit generalization to the higher dimensional cases. Also the $3\times 3$ matrix expression of the Lax operator is found, which have a well defined limit at $q\to 1$.

arXiv comment22 pages; references added, minor corrections done

References in corpus (10)

• The algebraic Bethe ansatz for rational braid-monoid lattice models
• An Intersecting Loop Model as a Solvable Super Spin Chain
• R-matrices and Spectrum of Vertex Models based on Superalgebras
• Integrable quantum field theories with OSP(m/2n) symmetries
• Integrable quantum field theories with supergroup symmetries: the $OSP(1/2)$ case
• Creation operators and Bethe vectors of the osp(1|2) Gaudin model
• Trigonometric osp(1|2) Gaudin model
• Exact solution of the simplest super-orthosymplectic invariant magnet
• Twisted Quantum Affine Superalgebra $U_q[gl(m|n{)}^{(2)}]$ and New $U_q[osp(m|n)]$ Invariant R-matrices
• Basic Hypergeometric Functions and Covariant Spaces for Even Dimensional Representations of U_q[osp(1/2)]

Cited by in corpus (7)

• On the solutions to the multi-parametric Yang-Baxter equations
• Dual description of $\eta$-deformed OSP sigma models
• Fusion Rules of the Lowest Weight Representations of osp_q(1|2) at Roots of Unity: Polynomial Realization and Degeneration at Roots of Unity
• New solutions to the $s{\ell }_q(2)$-invariant Yang-Baxter equations at roots of unity: cyclic representations
• New solutions to the $s{\ell }_q(2)$-invariant Yang-Baxter equations at roots of unity
• New series of multi-parametric solutions to GYBE: quantum gates and integrability
• Series of the solutions to Yang-Baxter equations: Hecke type matrices and descendant R-, L-operators