New solutions to the tetrahedron equation associated with quantized six-vertex models
arXiv:2208.10258 · doi:10.1007/s00220-023-04711-y
Abstract
We present a family of new solutions to the tetrahedron equation of the form , where operator may be regarded as a quantized six-vertex model whose Boltzmann weights are specific representations of the -oscillator or -Weyl algebras. When the three 's are associated with the -oscillator algebra, coincides with the known intertwiner of the quantized coordinate ring . On the other hand, 's based on the -Weyl algebra lead to new 's whose elements are either factorized or expressed as a terminating -hypergeometric type series.
22 pages, 4 figures. Minor revision