
SIGMA 13 (2017), 031, 14 pages arXiv:1505.06579
https://doi.org/10.3842/SIGMA.2017.031
Contribution to the Special Issue on Recent Advances in Quantum Integrable Systems
Zamolodchikov Tetrahedral Equation and Higher Hamiltonians of $2d$ Quantum Integrable Systems
Dmitry V. Talalaev
Geometry and Topology Department, Faculty of Mechanics and Mathematics, Moscow State University, Moscow, 119991 Russia
Received January 17, 2017, in final form May 13, 2017; Published online May 22, 2017
Abstract
The main aim of this work is to develop a method of constructing higher Hamiltonians of quantum integrable systems associated with the solution of the Zamolodchikov tetrahedral equation. As opposed to the result of V.V. Bazhanov and S.M. Sergeev the approach presented here is effective for generic solutions of the tetrahedral equation without spectral parameter. In a sense, this result is a twodimensional generalization of the method by J.M. Maillet. The work is a part of the project relating the tetrahedral equation with the quasiinvariants of 2knots.
Key words:
Zamolodchikov tetrahedral equation; quantum integrable systems; startriangle transformation.
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