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• W2074522650 abstract "Inönü–Wigner contractions from the rotation group O(n+1) to the Euclidean group E(n) are used to relate the separation of variables in Laplace–Beltrami operators on n-dimensional spheres and Euclidean spaces, respectively. In this article we consider all subgroup type coordinates corresponding to different chains of subgroups of O(n+1) and E(n), respectively. In particular, the contractions relate the graphical formalism of “trees” on spheres to the “clusters” on Euclidean spaces (introduced in this article). The contractions are considered analytically on several levels: the vector fields realizing the Lie algebras, the complete sets of commuting operators characterizing separable coordinate systems, the coordinate systems themselves and the separated eigenfunctions." @default.
• W2074522650 created "2016-06-24" @default.
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• W2074522650 date "1999-03-01" @default.
• W2074522650 modified "2023-10-01" @default.
• W2074522650 title "Contractions of Lie algebras and separation of variables. The n-dimensional sphere" @default.
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• W2074522650 doi "https://doi.org/10.1063/1.532820" @default.
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