Représentations irréductibles bornées des groupes de Lie exponentiels

Content Provider	Semantic Scholar
Author	Ludwig, Jean Pierre Molitor-Braun, Carine
Copyright Year	2001
Abstract	Let G be a solvable exponential Lie group. We characterize all the continuous topologically irreducible bounded representations (T,U) of G on a Banach space U by giving a G-orbit in n∗ (n being the nilradical of g), a topologically irreducible representation of L1(Rn, ω), for a certain weight ω and a certain n ∈ N, and a topologically simple extension norm. If G is not symmetric, i.e., if the weight ω is exponential, we get a new type of representations which are fundamentally different from the induced representations. Recu par les editeurs 12 novembre, 1999. Etude effectuee dans le cadre du projet de recherche MEN/CUL/98/007. Classification (AMS) par sujet: 43A20. Mots cles: groupe de Lie resoluble exponentiel, representation bornee topologiquement irreductible, orbite, norme d’extension, sous-espace invariant, ideal premier, ideal primitif. c ©Societe Mathematique du Canada 2001. 944
Starting Page	944
Ending Page	978
Page Count	35
File Format	PDF HTM / HTML
DOI	10.4153/cjm-2001-038-0
Volume Number	53
Alternate Webpage(s)	https://cms.math.ca/cjm/abstract/pdf/149337.pdf
Alternate Webpage(s)	https://doi.org/10.4153/cjm-2001-038-0
Language	English
Access Restriction	Open
Content Type	Text
Resource Type	Article