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 representa- tions 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 mul- tiplicative representations were monotonous. Here we show that all the other multiplicative representations are either odd or du- plicitous. The conjecture is therefore established for multiplicative representations.
Free group representations from vector-valued multiplicative functions, III / Gabriella Kuhn, M.; Saliani, Sandra; Steger, Tim. - (2020), pp. 1-28. [10.48550/arXiv.2010.06222]
Free group representations from vector-valued multiplicative functions, III
Tim StegerMembro del Collaboration Group
2020-01-01
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 representa- tions 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 mul- tiplicative representations were monotonous. Here we show that all the other multiplicative representations are either odd or du- plicitous. The conjecture is therefore established for multiplicative representations.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
