Journal of Lie Theory

no. 3
Decomposition and Multiplicities for Quasiregular Representations of Algebraic Solvable Lie Groups
Journal of Lie Theory, Volume 19 (2009) no. 3, pp. 557-612
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.
DOI: 10.5802/jolt.570
Classification: 22E45, 22E25, 43A25
Keywords: Quasiregular representation, coadjoint orbit, Plancherel formula, multiplicity function 
@article{JOLT_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},
     doi = {10.5802/jolt.570},
     zbl = {1187.22011},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.570/}
}
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B. N. Currey. Decomposition and Multiplicities for Quasiregular Representations of Algebraic Solvable Lie Groups. Journal of Lie Theory, Volume 19 (2009) no. 3, pp. 557-612. doi: 10.5802/jolt.570

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