Représentations irréductibles bornées des groupes de Lie exponentiels

Ludwig, J. ; Molitor-Braun, C.

Canadian journal of mathematics, Tome 53 (2001) no. 5, pp. 944-978

Résumé

Let $G$ be a solvable exponential Lie group. We characterize all the continuous topologically irreducible bounded representations $(T,\mathcal{U})$ of $G$ on a Banach space $\mathcal{U}$ by giving a $G$ -orbit in ${{n}^{*}}$ ( $\mathfrak{n}$ being the nilradical of $\mathfrak{g}$ ), a topologically irreducible representation of ${{L}^{1}}({{\mathbb{R}}^{n}},\,\,\omega )$ , for a certain weight $\omega $ and a certain $n\,\in \,\mathbb{N}$ , and a topologically simple extension norm. If $G$ is not symmetric, i.e., if the weight $\omega $ is exponential, we get a new type of representations which are fundamentally different from the induced representations.

Détail

DOI : 10.4153/CJM-2001-038-0

Mots-clés : 43A20, groupe de Lie résoluble exponentiel, représentation bornée topologiquement irréductible, orbite, norme d’extension, sous-espace invariant, idéal premier, idéal primitif

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