Journal of Lie Theory

no. 3
Decomposition and Multiplicities for Quasiregular Representations of Algebraic Solvable Lie Groups
Bradley N. Currey1
1Dept. of Mathematics and Computer Science, Saint Louis University, St. Louis, MO 63103, U.S.A.
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

Bradley N. Currey  1

1 Dept. of Mathematics and Computer Science, Saint Louis University, St. Louis, MO 63103, U.S.A. 
Bradley 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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