Abstract
Abstract We construct a new solution to the tetrahedron equation and the three-dimensional (3D) reflection equation by extending the quantum cluster algebra approach by Sun and Yagi concerning the former. We consider the Fock–Goncharov quivers associated with the longest elements of the Weyl groups of type $A$ and $C$, and investigate the cluster transformations corresponding to changing a reduced expression into a “most distant” one. By devising a new realization of the quantum $y$-variables in terms of $q$-Weyl algebra, the solutions are extracted as the operators whose adjoint actions yield the cluster transformations of the quantum $y$-variables. Explicit formulas of their matrix elements are also derived for some typical representations.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
