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arXiv · 1405.5506

Integrable systems from the classical reflection equation

Gus Schrader
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Abstract

We construct integrable Hamiltonian systems on $G/K$, where $G$ is a quasitriangular Poisson Lie group and $K$ is a Lie subgroup arising as the fixed point set of a group automorphism $σ$ of $G$ satisfying the classical reflection equation. In the case that $G$ is factorizable, we show that the time evolution of these systems is described by a Lax equation, and present its solution in terms of a factorization problem in $G$. Our construction is closely related to the semiclassical limit of Sklyanin's integrable quantum spin chains with reflecting boundaries.

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Gus Schrader. 2015-06-08. Integrable systems from the classical reflection equation. https://doi.org/10.1093/imrn%2Frnv113

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