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

## TL;DR

This paper generalizes Sklyanin's spectral coordinates to Calogero-Moser spaces associated with cyclic quivers, providing explicit rational functions that relate spectral and conjugate variables, and demonstrating their well-definedness on type A singularities.

## Contribution

It introduces a new construction of canonical spectral coordinates for Calogero-Moser spaces linked to cyclic quivers, extending previous results to a broader class.

## Key findings

- Canonical spectral coordinates are well-defined on type A singularities.
- Constructed rational functions interpolate between spectral and conjugate variables.
- Generalized Sklyanin's formula to cyclic quiver cases.

## 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.