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

Explore new solutions to the tetrahedron equation RLLL = LLLR in this 41-minute lecture from the Workshop on Integrable systems, exactly solvable models and algebras. Delve into a family of solutions where L represents a quantized six-vertex model with Boltzmann weights as specific representations of q-oscillator or q-Weyl algebras. Examine how R coincides with the known intertwiner of the quantized coordinate ring Aq(sl3) when L's are associated with the q-oscillator algebra. Investigate new R's derived from L's based on the q-Weyl algebra, featuring elements that are either factorized or expressed as terminating q-hypergeometric type series. Learn about the confirmation of the RRRR=RRRR type tetrahedron equation in various cases, based on joint work with S. Matsuike and A. Yoneyama.

Atsuo Kuniba: New solutions to the tetrahedron equation associated with quantized six-vertex models