Publisher： Cambridge University Press
E-ISSN： 1755-1633|42|2|293-306
ISSN： 0004-9727
Source： Bulletin of the Australian Mathematical Society, Vol.42, Iss.2, 1990-10, pp. : 293-306
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Abstract
An orbital integral formula is proven for the direct integral decomposition of an induced representation of a connected nilpotent Lie group. Previous work required simple connectivity. An explicit description of the spectral measure and spectral multiplicity function is derived in terms of orbital parameters. It is also proven that connected (but not necessarily simply connected) exponential solvable symmetric spaces are multiplicity free. Finally, the qualitative properties of the spectral multiplicity function are examined via several illuminating examples.
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