Lower Multiplicity for Irreducible Representations of Nilpotent Locally Compact Groups

✍ Scribed by Eberhard Kaniuth

• Publisher: Elsevier Science
• Year: 1999
• Tongue: English
• Weight: 141 KB
• Volume: 168
• Category: Article
• ISSN: 0022-1236
• DOI: 10.1006/jfan.1999.3469

✦ Synopsis

Let G be a nilpotent locally compact group. The lower multiplicity M L (?) is defined for every irreducible representation ? of G, which does not form an open point in the dual space G of G. It is shown that M L (?)=1 if either G is connected or ? is finite dimensional. Conversely, for G a nilpotent group with small invariant neighbourhoods, M L (?)< implies that ? is finite dimensional.