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Decomposition of Quasi-regular Representations Induced from Discrete Subgroups of Nilpotent Lie Groups

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Abstract

We describe the direct integral decomposition of a quasi regular representation of a connected and simply connected nilpotent Lie group G, which is induced from a discrete subgroup Γ. The solution is given explicitly in terms of orbital parameters. That is, the spectrum, multiplicity and spectral measure that constitute the decomposition are described completely in terms of natural objects associated to the co-adjoint orbits of G. We conclude with a study of the multiplicity function in certain cases.

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  1. Department of Mathematics, Faculty of Sciences at Sfax, Route Soukra, B.P. 802, 3018, Sfax, Tunisia

    Hatem Hamrouni

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  1. Hatem Hamrouni
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Correspondence to Hatem Hamrouni.

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Hamrouni, H. Decomposition of Quasi-regular Representations Induced from Discrete Subgroups of Nilpotent Lie Groups. Lett Math Phys 81, 135–150 (2007). https://doi.org/10.1007/s11005-007-0176-9

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