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.
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This paper is dedicated to Joe Wolf, in honor of all that we have learned from him about the connections among geometry, representation theory, and harmonic analysis; and in gratitude for wonderful years of friendship.
Peter E. Trapa was supported in part by NSF Grant DMS-1302237.
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Schlichtkrull, H., Trapa, P.E. & Vogan, D.A. Laplacians on spheres. São Paulo J. Math. Sci. 12, 295–358 (2018). https://doi.org/10.1007/s40863-018-0100-5
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DOI: https://doi.org/10.1007/s40863-018-0100-5