Ref HAL: hal-01820521_v1
Ref Arxiv: 1803.09931
DOI: 10.1007/s11005-018-1128-2
WoS: 000460657200005
Ref. & Cit.: NASA ADS
Exporter : BibTex | endNote
1 Citation
Résumé:

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 .

Commentaires: 12 pages. References added. Explicit relation between our non-skew symmetric r-matrices and standard rational r-matrix given in the Gaudin models section