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arXiv · 1803.09931

Classical $N$-Reflection Equation and Gaudin Models

Vincent Caudrelier·Nicolas Crampe
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Abstract

We introduce the notion of $N$-reflection equation which provides a large generalization of the usual classical reflection equation describing integrable boundary conditions. The latter is recovered as a special example of the $N=2$ case. The basic theory is established and illustrated with several examples of solutions of the $N$-reflection equation associated to the rational and trigonometric $r$-matrices. A central result is the construction of a Poisson algebra associated to a non skew-symmetric $r$-matrix whose form is specified by a solution of the $N$-reflection equation. Generating functions of quantities in involution can be identified within this Poisson algebra. As an application, we construct new classical Gaudin-type Hamiltonians, particular cases of which are Gaudin Hamiltonians of $BC_L$-type .

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Vincent Caudrelier, Nicolas Crampe. 2018-03-27. Classical $N$-Reflection Equation and Gaudin Models. https://doi.org/10.1007/s11005-018-1128-2

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