Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Plancherel Formulae associated to Filtrations of Nilpotent Lie Groups   We study the conditions for a nilpotent Lie group to be foliated into
subgroups that have square integrable (relative discrete series) unitary
representations, that fit together to form a filtration by normal subgroups.
Then we use that filtration to construct a class of "stepwise square
integrable" representations on which Plancherel measure is concentrated.
Further, we work out the character formulae for those stepwise square
integrable representations, and we give an explicit Plancherel formula. Next,
we use some structure theory to check that all these constructions and results
apply to nilradicals of minimal parabolic subgroups of real reductive Lie
groups. Finally, we develop multiplicity formulae for compact quotients
$N/\Gamma$ where $\Gamma$ respects the filtration.

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The categories of this paper are: hep-ex
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The categories of this paper are: gr-qc
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The categories of this paper are: cond-mat
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The categories of this paper are: chao-dyn
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The categories of this paper are: dg-ga
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The categories of this paper are: chem-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: physics
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The categories of this paper are: cs
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The categories of this paper are: q-alg
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The categories of this paper are: hep-th
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The categories of this paper are: hep-lat
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The categories of this paper are: q-bio
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The categories of this paper are: comp-gas
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The categories of this paper are: patt-sol
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The categories of this paper are: atom-ph