KP hierarchy for the cyclic quiver

Understand

We introduce a generalisation of the KP hierarchy, closely related to the cyclic quiver and the Cherednik algebra $H_k(\mathbb Z_m)$.

• 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 G.
• Wilson, we show that our hierarchy admits solutions parameterised by suitable quiver varieties.