Series of the solutions to Yang-Baxter equations: Hecke type matrices and descendant R-, L-operators

Abstract

We have constructed series of the spectral parameter dependent solutions to the Yang-Baxter equations defined on the tensor product of reducible representations with symmetry of quantum algebra. These series are produced as descendant solutions from the $s{l}_q(2)$-invariant Hecke type $R^{rr}(u)$-matrices. The analogues of the matrices of Hecke type with the symmetry of the quantum super-algebra $os{p}_q(1|2)$ are obtained precisely. For the homogeneous solutions $R^{r^2-1r^2-1}$ there are constructed Hamiltonian operators of the corresponding one-dimensional quantum integrable models, which describe rather intricate interactions between different kind of spin states. Centralizer operators defined on the products of the composite states are discussed. The inhomogeneous series of the operators $R^{r\mathcal{R}}(u)$, extended Lax operators of Hecke type, also are suggested.

36 pages; corrected typos, made some clarifications; the printed version

References in corpus (4)

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

Cited by in corpus (1)

• New series of multi-parametric solutions to GYBE: quantum gates and integrability