Trigonometric and elliptic Ruijsenaars-Schneider systems on the complex projective space

Abstract

We present a direct construction of compact real forms of the trigonometric and elliptic $n$-particle Ruijsenaars-Schneider systems whose completed center-of-mass phase space is the complex projective space ${\mathbb{CP}}^{n-1}$ with the Fubini-Study symplectic structure. These systems are labelled by an integer $p\in \{1,\dots ,n-1\}$ relative prime to $n$ and a coupling parameter $y$ varying in a certain punctured interval around $p\pi /n$. Our work extends Ruijsenaars's pioneering study of compactifications that imposed the restriction $0<y<\pi /n$, and also builds on an earlier derivation of more general compact trigonometric systems by Hamiltonian reduction.

18 pages, v2(published version): minor improvement in the text, no change in equations

References in corpus (2)

• The supersymmetric Ruijsenaars-Schneider model
• Lax representation of the hyperbolic van Diejen dynamics with two coupling parameters

Cited by in corpus (5)

• Elliptic Ruijsenaars difference operators on bounded partitions
• Kähler geometry for $su(1,N|M)$-superconformal mechanics
• Quantization and explicit diagonalization of new compactified trigonometric Ruijsenaars-Schneider systems
• Eigenfunctions of a discrete elliptic integrable particle model with hyperoctahedral symmetry
• Elliptic Ruijsenaars difference operators, symmetric polynomials, and Wess-Zumino-Witten fusion rings