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Harmonics on hyperspheres, separation of variables and the bethe ansatz (1995)

Harnad, J. ; Winternitz, P.

Springer

Letters in mathematical physics 33 (1995), S. 61-74

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ISSN: 1573-0530

Keywords: 81R99 ; 82B23 ; 17B65 ; 35J05 ; 34A26

Source: Springer Online Journal Archives 1860-2000

Topics: Mathematics , Physics

Notes: Abstract The relation between solutions to Helmholtz's equation on the sphereS n-1 and the $$[\mathfrak{s}\mathfrak{l}(2)]^n $$ n Gaudin spin chain is clarified. The joint eigenfunctions of the Laplacian and a complete set of commuting second-order operators suggested by theR-matrix approach to integrable systems, based on the loop algebra $$\widetilde{\mathfrak{s}\mathfrak{l}}(2)_R $$ , are found in terms of homogeneous polynomials in the ambient space. The relation of this method of determining a basis of harmonic functions onS n-1 to the Bethe ansatz approach to integrable systems is explained.

Type of Medium: Electronic Resource

URL: http://dx.doi.org/10.1007/BF00750812

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