KP hierarchy for the cyclic quiver

We introduce a generalisation of the KP hierarchy, closely related to the cyclic quiver and the Cherednik algebra Hk(Zm). This hierarchy depends on m parameters (one of which can be eliminated), with the usual KP hierarchy corresponding to the m = 1 case. Generalising the result of Wilson [Invent. Math. 133(1), 1–41 (1998)], we show that our hierarchy admits solutions parameterised by suitable quiver varieties. The pole dynamics for these solutions is shown to be governed by the classical Calogero–Moser system for the wreath-product Zm≀Sn and its new spin version. These results are further extended to the case of the multi-component hierarchy.