
Journal of Lie Theory 19 (2009), No. 3, 557612 Copyright Heldermann Verlag 2009 Decomposition and Multiplicities for Quasiregular Representations of Algebraic Solvable Lie Groups Bradley N. Currey Dept. of Mathematics and Computer Science, Saint Louis University, St. Louis, MO 63103, U.S.A. curreybn@slu.edu We obtain an explicit irreducible decomposition for the quasiregular representation τ of a connected algebraic solvable Lie group induced from a conormal Levi factor. In the case where the multiplicity function is unbounded, we show that τ is a finite direct sum of subrepresentations τ_{ε} where for each ε, τ_{ε} 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. Keywords: Quasiregular representation, coadjoint orbit, Plancherel formula, multiplicity function. MSC: 22E45, 22E25; 43A25 [ Fulltextpdf (424 KB)] for subscribers only. 