Abstract
We develop a technique for the construction of integrable models with a ℤ2 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 is found. We analyze in details the N = 2 case and find the corresponding quantum group behind this solution. It can be regarded as the quantum group UqB(gl(2)), with a matrix deformation parameter qB such that (qB)2 = q2. The symmetry behind these models can also be interpreted as the tensor product of the (-1)-Weyl algebra by an extension of Uq(gl(N)) with a Cartan generator related to deformation parameter -1.
Original language | English (US) |
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Pages (from-to) | 209-222 |
Number of pages | 14 |
Journal | Letters in Mathematical Physics |
Volume | 58 |
Issue number | 3 |
DOIs | |
State | Published - Dec 2001 |
Externally published | Yes |
Bibliographical note
Funding Information:The authors, A.S. and T.S., acknowledge the LAPTH for hospitality, where this work was carried out. T.S. also acknowledges INTAS grant 99-1459 and A.S acknowledges the partial ¢nancial support of grant 00-390.
Keywords
- Bethe Ansatz
- Integrable models
- Ladder models
- Quantum groups
- Staggered parameters