Canonical spectral coordinates for the CalogeroMoser space associated with the cyclic quiver
Abstract
Sklyanin's formula provides a set of canonical spectral coordinates on the standard CalogeroMoser space associated with the quiver consisting of a vertex and a loop. We generalize this result to CalogeroMoser spaces attached to cyclic quivers by constructing rational functions that relate spectral coordinates to conjugate variables. These canonical coordinates turn out to be welldefined on the corresponding simple singularity of type $A$, and the rational functions we construct define interpolating polynomials between them.
 Publication:

arXiv eprints
 Pub Date:
 December 2018
 DOI:
 10.48550/arXiv.1812.02544
 arXiv:
 arXiv:1812.02544
 Bibcode:
 2018arXiv181202544G
 Keywords:

 Mathematical Physics;
 Mathematics  Algebraic Geometry;
 Nonlinear Sciences  Exactly Solvable and Integrable Systems;
 14H70;
 37J15;
 53D20
 EPrint:
 20 pages, 3 figures