Solutions of 3D Reflection Equation from Quantum Cluster Algebra Associated with Symmetric Butterfly Quiver
Quantum Algebra
2025-12-29 v1 Mathematical Physics
math.MP
Exactly Solvable and Integrable Systems
Abstract
We construct a new solution to the three-dimensional reflection equation, a boundary analogue of the tetrahedron equation. The -operator is the one obtained by Sun, Terashima, Yagi, and the authors in 2024, involving four quantum dilogarithms with arguments in the -Weyl algebra. The new -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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Cite
@article{arxiv.2512.22004,
title = {Solutions of 3D Reflection Equation from Quantum Cluster Algebra Associated with Symmetric Butterfly Quiver},
author = {Rei Inoue and Atsuo Kuniba},
journal= {arXiv preprint arXiv:2512.22004},
year = {2025}
}
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54 pages