The Laplacian on homogeneous spaces

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dc.creatorHu, Liangzhong
dc.date2008-05-16
dc.date.accessioned2026-07-07T11:50:51Z
dc.date.available2026-07-07T11:50:51Z
dc.descriptionThe solution of the eigenvalue problem of the Laplacian on a general homogeneous space G/H is given. Here, G is a compact, semisimple Lie group, H is a closed subgroup of G, and the rank of H is equal to the rank of G. It is shown that the multiplicity of the lowest eigenvalue of the Laplacian on G/H is just the degeneracy of the lowest Landau level for a particle moving on G/H in the presence of the background gauge field. Moreover, the eigenspace of the lowest eigenvalue of the Laplacian on G/H is, up to a sign, equal to the G-equivariant index of the Dirac operator of Kostant on G/H.
dc.identifierhttps://arxiv.org/abs/0805.2531
dc.identifierhttp://arxiv.org/abs/0805.2531
dc.identifierJ.Math.Phys.49:053513,2008
dc.identifierdoi:10.1063/1.2924268
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/203700
dc.subjectMathematical Physics
dc.subjectMesoscale and Nanoscale Physics
dc.subjectHigh Energy Physics - Theory
dc.subjectRepresentation Theory
dc.titleThe Laplacian on homogeneous spaces
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