Chalykh, O orcid.org/0000-0003-4529-2310 and Silantyev, A (2017) KP hierarchy for the cyclic quiver. Journal of Mathematical Physics, 58 (7). 071702. ISSN 0022-2488
Abstract
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.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | Published by AIP Publishing. This article may be downloaded for personal use only. Any other use requires prior permission of the author and AIP Publishing. The following article appeared in Chalykh, O and Silantyev, A (2017) KP hierarchy for the cyclic quiver. Journal of Mathematical Physics, 58. 071702. ISSN 0022-2488, and may be found at https://doi.org/10.1063/1.4991031. Reproduced in accordance with the publisher's self-archiving policy. |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Mathematics (Leeds) > Applied Mathematics (Leeds) |
Funding Information: | Funder Grant number EPSRC (Engineering and Physical Sciences Research Council) EP/K004999/1 |
Depositing User: | Symplectic Publications |
Date Deposited: | 14 Jul 2017 12:44 |
Last Modified: | 09 Sep 2020 16:36 |
Status: | Published |
Publisher: | American Institute of Physics |
Identification Number: | 10.1063/1.4991031 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:119027 |