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The Plancherel Formula for an Inhomogeneous Vector Group

Abstract : We give a concrete realization of the Plancherel measure for a semi-direct product N⋊H where N and H are vector groups for which the linear action of H on N is almost everywhere regular. A procedure using matrix reductions produces explicit (orbital) parameters by which a continuous field of unitary irreducible representations is realized and the almost all of the dual space of N⋊H naturally has the structure of a smooth manifold. Using the simplest possible field of positive semi-invariant operators, the Plancherel measure is obtained via an explicit volume form on a smooth cross-section Σ for almost all H-orbits. The associated trace characters are also shown to be tempered distributions.
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Soumis le : mardi 17 décembre 2019 - 15:30:46
Dernière modification le : vendredi 25 novembre 2022 - 10:12:06




Didier Arnal, Bradley Currey, Bechir Dali. The Plancherel Formula for an Inhomogeneous Vector Group. Journal of Fourier Analysis and Applications, 2019, 25 (6), pp.2837-2876. ⟨10.1007/s00041-019-09684-y⟩. ⟨hal-02416178⟩



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