Journal of Nonlinear Mathematical Physics

Volume 27, Issue 2, January 2020, Pages 243 - 266

Canonical spectral coordinates for the Calogero-Moser space associated with the cyclic quiver

Authors
Tamás Görbe
School of Mathematics, University of Leeds Leeds, LS2 9JT, UK,T.Gorbe@leeds.ac.uk
Ádám Gyenge
Mathematical Institute, University of Oxford Andrew Wiles Building, Radcliffe Observatory Quarter Woodstock Road OX2 6GG, Oxford, UK,Adam.Gyenge@maths.ox.ac.uk
Received 3 February 2019, Accepted 29 August 2019, Available Online 27 January 2020.
DOI
10.1080/14029251.2020.1700634How to use a DOI?
Keywords
Calogero-Moser; cyclic quiver; Darboux coordinates; canonical spectral coordinates; Sklyanin’s formula
Abstract

Sklyanin’s formula provides a set of canonical spectral coordinates on the standard Calogero-Moser space associated with the quiver consisting of a vertex and a loop. We generalize this result to Calogero-Moser spaces attached to cyclic quivers by constructing rational functions that relate spectral coordinates to conjugate variables. These canonical coordinates turn out to be well-defined on the corresponding simple singularity of type A, and the rational functions we construct define interpolating polynomials between them.

Copyright
© 2020 The Authors. Published by Atlantis and Taylor & Francis
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

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Journal
Journal of Nonlinear Mathematical Physics
Volume-Issue
27 - 2
Pages
243 - 266
Publication Date
2020/01/27
ISSN (Online)
1776-0852
ISSN (Print)
1402-9251
DOI
10.1080/14029251.2020.1700634How to use a DOI?
Copyright
© 2020 The Authors. Published by Atlantis and Taylor & Francis
Open Access
This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

Cite this article

TY  - JOUR
AU  - Tamás Görbe
AU  - Ádám Gyenge
PY  - 2020
DA  - 2020/01/27
TI  - Canonical spectral coordinates for the Calogero-Moser space associated with the cyclic quiver
JO  - Journal of Nonlinear Mathematical Physics
SP  - 243
EP  - 266
VL  - 27
IS  - 2
SN  - 1776-0852
UR  - https://doi.org/10.1080/14029251.2020.1700634
DO  - 10.1080/14029251.2020.1700634
ID  - Görbe2020
ER  -