Generalization of the U_q(gl(N)) algebra and staggered models

Details Generalization of the U_q(gl(N)) algebra and staggered models Generalization of the U_q(gl(N)) algebra and staggered models

2001-06-15

arxiv.org/abs/hep-th/0106139v1

Lett.Math.Phys. 58 (2001) 209-222

Physics

High Energy Physics

High Energy Physics - Theory

12 pages ; Latex2e

Scientific paper

10.1023/A:1014504526934

We develop a technique of construction of integrable models with a Z_2 grading of both the auxiliary (chain) and quantum (time) spaces. These models have a staggered disposition of the anisotropy parameter. The corresponding Yang-Baxter Equations are written down and their solution for the gl(N) case are found. We analyze in details the N=2 case and find the corresponding quantum group behind this solution. It can be regarded as quantum U_{q,B}(gl(2)) group with a matrix deformation parameter qB with (qB)^2=q^2. The symmetry behind these models can also be interpreted as the tensor product of the (-1)-Weyl algebra by an extension of U_q(gl(N)) with a Cartan generator related to deformation parameter -1.

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