Hyperspherical harmonics, separation of variables and the Bethe ansatz

Harnad, John P.; Winternitz, P.

doi:10.1007/BF00750812

Hyperspherical harmonics, separation of variables and the Bethe ansatz

John P. Harnad
(
- Concordia U., Math. Dept. and
- Montreal U., CRM
)
,
P. Winternitz
(
- Montreal U., CRM
)

May 16, 1994

14 pages

Published in:

Lett.Math.Phys. 33 (1995) 61-74

e-Print:

hep-th/9405085 [hep-th]

DOI:

10.1007/BF00750812

Report number:

CRM-2174

View in:

pdf

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Abstract: (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.

Note:

14 pgs, Plain Tex, preprint CRM--2174 (May, 1994)

References(29)

Figures(0)

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