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arXiv · 1512.08551

KP hierarchy for the cyclic quiver

Oleg Chalykh·Alexey Silantyev
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Abstract

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. The pole dynamics for these solutions is shown to be governed by the classical Calogero-Moser system for the wreath-product $\mathbb Z_m\wr S_n$ and its new spin version. These results are further extended to the case of the multi-component hierarchy.

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Oleg Chalykh, Alexey Silantyev. 2015-12-28. KP hierarchy for the cyclic quiver. https://arxiv.org/abs/1512.08551

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