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

D. Arnaudon, A. Sedrakyan, T. Sedrakyan, P. Sorba

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5 Scopus citations

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 languageEnglish (US)
Pages (from-to)209-222
Number of pages14
JournalLetters in Mathematical Physics
Volume58
Issue number3
DOIs
StatePublished - Dec 2001

Keywords

  • Bethe Ansatz
  • Integrable models
  • Ladder models
  • Quantum groups
  • Staggered parameters

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