Abstract. Let π be an irreducible unitary representation of a finitely generated nonabelian free group Γ; suppose π is weakly contained in the regular representation. In 2001 the first and third authors conjectured that such a representation must be either odd or monotonous or duplicitous. In 2004 they introduced the class of multiplicative representations: this is a large class of representations obtained by looking at the action of Γ on its Cayley graph. In the second paper of this series we showed that some of the multiplicative representations were monotonous. Here we show that all the other multiplicative representations are either odd or duplicitous. The conjecture is therefore established for multiplicative representations.

Kuhn, M., Saliani, S., Steger, T. (In corso di stampa). Free group representations from vector-valued multiplicative functions, III. ISRAEL JOURNAL OF MATHEMATICS.

Free group representations from vector-valued multiplicative functions, III

Kuhn, MG;
In corso di stampa

Abstract

Abstract. Let π be an irreducible unitary representation of a finitely generated nonabelian free group Γ; suppose π is weakly contained in the regular representation. In 2001 the first and third authors conjectured that such a representation must be either odd or monotonous or duplicitous. In 2004 they introduced the class of multiplicative representations: this is a large class of representations obtained by looking at the action of Γ on its Cayley graph. In the second paper of this series we showed that some of the multiplicative representations were monotonous. Here we show that all the other multiplicative representations are either odd or duplicitous. The conjecture is therefore established for multiplicative representations.
Articolo in rivista - Articolo scientifico
Irreducible unitary representations; Free groups; Boundary realization; Duplicity; Oddity;
English
Kuhn, M., Saliani, S., Steger, T. (In corso di stampa). Free group representations from vector-valued multiplicative functions, III. ISRAEL JOURNAL OF MATHEMATICS.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/347973
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