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Laplacians on spheres. (English) Zbl 1405.43007
Authors’ abstract: Spheres can be written as homogeneous spaces $$G/H$$ for compact Lie groups in a small number of ways. In each case, the decomposition of $$L^2(G/H)$$ into irreducible representations of $$G$$ contains interesting information. We recall these decompositions, and see what they can reveal about the analogous problem for noncompact real forms of $$G$$ and $$H$$.

##### MSC:
 43A85 Harmonic analysis on homogeneous spaces 22E45 Representations of Lie and linear algebraic groups over real fields: analytic methods
##### Software:
Atlas of Lie Groups
Full Text:
##### References:
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