Abstract
For each compact Lie algebra g and each real representationV of g we construct a two-step nilpotent Lie groupN(g, V), endowed with a natural left-invariant riemannian metric. The main goal of this paper is to show that this construction produces many new Gelfand pairs associated with nilpotent Lie groups. Indeed, we will give a full classification of the manifoldsN(g, V) which are commutative spaces, using a characterization in terms of multiplicity-free actions.
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Supported by a fellowship from CONICET and research grants from CONICOR and SeCyT UNC (Argentina).
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Lauret, J. Gelfand pairs attached to representations of compact Lie groups. Transformation Groups 5, 307–324 (2000). https://doi.org/10.1007/BF01234795
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DOI: https://doi.org/10.1007/BF01234795