New Solutions to the Tetrahedron Equation Associated with Quantized Six-Vertex Models

Abstract

AbstractWe present a family of new solutions to the tetrahedron equation of the form $$RLLL=LLLR$$ R L L L = L L L R , where L operator may be regarded as a quantized six-vertex model whose Boltzmann weights are specific representations of the q-oscillator or q-Weyl algebras. When the three L’s are associated with the q-oscillator algebra, R coincides with the known intertwiner of the quantized coordinate ring $$A_q(sl_3)$$ A q ( s l 3 ) . On the other hand, L’s based on the q-Weyl algebra lead to new R’s whose elements are either factorized or expressed as a terminating q-hypergeometric type series.