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<p>The main result of this paper is an explicit description of the stratification of the phase space of Calogero–Moser–Sutherland (CMS) integrable systems corresponding to Lie groups <i>SU</i>(<i>n</i>). The phase space decomposes into symplectic strata of dimensions 2<i>s</i>, where <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(s = 0, 1, \ldots , n - 1\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>s</mi> <mo>=</mo> <mn>0</mn> <mo>,</mo> <mn>1</mn> <mo>,</mo> <mo>…</mo> <mo>,</mo> <mi>n</mi> <mo>-</mo> <mn>1</mn> </mrow> </math></EquationSource> </InlineEquation>. On each stratum of the positive dimension, we construct natural action-angle coordinates and compute the symplectic form explicitly, showing that every stratum is symplectomorphic to <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\mathbb {R}_{&gt; 0}^s \times \mathbb {T}^s\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msubsup> <mi mathvariant="double-struck">R</mi> <mrow> <mo>&gt;</mo> <mn>0</mn> </mrow> <mi>s</mi> </msubsup> <mo>×</mo> <msup> <mrow> <mi mathvariant="double-struck">T</mi> </mrow> <mi>s</mi> </msup> </mrow> </math></EquationSource> </InlineEquation>. The zero-dimensional stratum corresponds to the equilibrium point of the multi-time CMS dynamics.</p>

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Low-dimensional tori in Calogero–Moser–Sutherland systems

  • 期刊论文

  • 发表日期：

    2026年3月27日

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  • Andrii Liashyk,
  • Guorui Ma,
  • Nicolai Reshetikhin,
  • Ivan Sechin

摘要

The main result of this paper is an explicit description of the stratification of the phase space of Calogero–Moser–Sutherland (CMS) integrable systems corresponding to Lie groups SU(n). The phase space decomposes into symplectic strata of dimensions 2s, where \(s = 0, 1, \ldots , n - 1\) s = 0 , 1 , … , n - 1 . On each stratum of the positive dimension, we construct natural action-angle coordinates and compute the symplectic form explicitly, showing that every stratum is symplectomorphic to \(\mathbb {R}_{> 0}^s \times \mathbb {T}^s\) R > 0 s × T s . The zero-dimensional stratum corresponds to the equilibrium point of the multi-time CMS dynamics.