Solutions of 3D Reflection Equation from Quantum Cluster Algebra Associated with Symmetric Butterfly Quiver
Abstract
We construct a new solution (R,K) to the three-dimensional reflection equation, a boundary analogue of the tetrahedron equation. The R-operator is the one obtained by Sun, Terashima, Yagi, and the authors in 2024, involving four quantum dilogarithms with arguments in the q-Weyl algebra. The new K-operator similarly involves ten such quantum dilogarithms. Our approach is based on the quantum cluster algebra associated with the symmetric butterfly quiver on the wiring diagram of type C.
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