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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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 -