Geodesic
Decomposition and Multiplicities for Quasiregular Representations of Algebraic Solvable Lie Groups
Journal of Lie theory, Tome 19 (2009) no. 3, pp. 557-612 Cet article a éte moissonné depuis la source Heldermann Verlag

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We obtain an explicit irreducible decomposition for the quasiregular representation τ of a connected algebraic solvable Lie group induced from a co-normal Levi factor. In the case where the multiplicity function is unbounded, we show that τ is a finite direct sum of subrepresentations τε where for each ε, τε is either infinite or has finite but unbounded multiplicity. We obtain a criterion by which the cases of bounded multiplicity, finite unbounded multiplicity, and infinite multiplicity are distinguished.
Classification : 22E45, 22E25, 43A25
Mots-clés : Quasiregular representation, coadjoint orbit, Plancherel formula, multiplicity function 
@article{JLT_2009_19_3_JLT_2009_19_3_a8,
     author = {B. N. Currey },
     title = {Decomposition and {Multiplicities} for {Quasiregular} {Representations} of {Algebraic} {Solvable} {Lie} {Groups}},
     journal = {Journal of Lie theory},
     pages = {557--612},
     year = {2009},
     volume = {19},
     number = {3},
     url = {http://geodesic.mathdoc.fr/item/JLT_2009_19_3_JLT_2009_19_3_a8/}
}
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B. N. Currey . Decomposition and Multiplicities for Quasiregular Representations of Algebraic Solvable Lie Groups. Journal of Lie theory, Tome 19 (2009) no. 3, pp. 557-612. http://geodesic.mathdoc.fr/item/JLT_2009_19_3_JLT_2009_19_3_a8/