Bethe Equations for a g_2 Model

We prove, using the coordinate Bethe ansatz, the exact solvability of a model of three particles whose point-like interactions are determined by the root system of g_2. The statistics of the wavefunction are left unspecified. Using the properties of the Weyl group, we are also able to find Bethe equations. It is notable that the method relies on a certain generalized version of the well-known Yang-Baxter equation. A particular class of non-trivial solutions to this equation emerges naturally