Stratified Superintegrability of Spin Calogero-Moser-Sutherland Systems
Abstract
We study the Poisson chain of the compact spin Calogero-Moser-Sutherland system obtained by conjugation reduction of T*SU(n) at a fixed coadjoint orbit. We give a Horn-type condition ensuring that the spectral torus acts freely on the full fiber over a simple spectrum; for each orbit, the admissible spectra form a nonempty open dense set, and the restricted chain is strongly superintegrable of rank n−1 on every orbit-type stratum. We also construct, across certain affine spectral walls, a proper quotient map onto a Hausdorff stratified Poisson space with a finite Whitney stratification. For SU(3), we compute the free spectral domain and the quotient near two intersecting walls, and a zero-orbit example shows that the analogous quotient need not be Hausdorff on the unrestricted reduced phase space.
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BibTeX
@misc{ma2026stratified,
title = {{Stratified Superintegrability of Spin Calogero-Moser-Sutherland Systems}},
author = {Guorui Ma and Junze Zhang},
howpublished = {arXiv},
year = {2026},
month = nov,
doi = {10.48550/arxiv.2611.01002},
eprint = {2611.01002},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2611.01002},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Stratified Superintegrability of Spin Calogero-Moser-Sutherland Systems
AU - Guorui Ma
AU - Junze Zhang
PY - 2026
DA - 2026/11/01
PB - arXiv
DO - 10.48550/arxiv.2611.01002
UR - https://arxiv.org/abs/2611.01002
AB - We study the Poisson chain of the compact spin Calogero-Moser-Sutherland system obtained by conjugation reduction of T^*SU(n) at a fixed coadjoint orbit. We give a Horn-type condition ensuring that the spectral torus acts freely on the full fiber over a simple spectrum; for each orbit, the admissible spectra form a nonempty open dense set, and the restricted chain is strongly superintegrable of rank n−1 on every orbit-type stratum. We also construct, across certain affine spectral walls, a proper quotient map onto a Hausdorff stratified Poisson space with a finite Whitney stratification. For SU(3), we compute the free spectral domain and the quotient near two intersecting walls, and a zero-orbit example shows that the analogous quotient need not be Hausdorff on the unrestricted reduced phase space.
ER -