Hyperspherical Harmonics, Separation of Variables and the Bethe Ansatz
Harnad, J. ; Winternitz, P.
arXiv, 9405085 / Harvested from arXiv
Text on arXiv
The relation between solutions to Helmholtz's equation on the sphere $S^{n-1}$ and the $[{\gr sl}(2)]^n$ Gaudin spin chain is clarified. The joint eigenfuctions of the Laplacian and a complete set of commuting second order operators suggested by the $R$--matrix approach to integrable systems, based on the loop algebra $\wt{sl}(2)_R$, are found in terms of homogeneous polynomials in the ambient space. The relation of this method of determining a basis of harmonic functions on $S^{n-1}$ to the Bethe ansatz approach to integrable systems is explained.
Publié le : 1994-05-12
Classification:  High Energy Physics - Theory,  Mathematical Physics 
@article{9405085,
     author = {Harnad, J. and Winternitz, P.},
     title = {Hyperspherical Harmonics, Separation of Variables and the Bethe Ansatz},
     journal = {arXiv},
     volume = {1994},
     number = {0},
     year = {1994},
     language = {en},
     url = {http://dml.mathdoc.fr/item/9405085}
}

Harnad, J.; Winternitz, P. Hyperspherical Harmonics, Separation of Variables and the Bethe Ansatz. arXiv, Tome 1994 (1994) no. 0, . http://gdmltest.u-ga.fr/item/9405085/