Vector version of Matsuo-Cherednik equation for the root system \(G_ 2\) (Q1916643)

In the paper [Invent. Math. 110, 95-121 (1992; Zbl 0801.35131)] \textit{A. Matsuo} introduced a system of differential equations associated with an arbitrary root system and showed that this is integrable and Weyl group invariant. He also gave a vector version of the equations for the root system of type \(A\). The vector versions for the root systems \(B\), \(C\) and \(D\) are given by \textit{V. A. Golubeva} and \textit{V. P. Leksin} [Short Communications of ICM, Zürich (1994)]. In the present note the authors give the vector version of the equations for the root system \(G_2\).