Let pi be an irreducible unitary representation of a finitely generated non-abelian free group Gamma; suppose pi 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 Gamma 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.

Free group representations from vector-valued multiplicative functions. III / Kuhn, M. G.; Saliani, S.; Steger, T.. - In: ISRAEL JOURNAL OF MATHEMATICS. - ISSN 0021-2172. - 258:1(2023), pp. 339-373. [10.1007/s11856-023-2474-z]

Free group representations from vector-valued multiplicative functions. III

Steger T.
Membro del Collaboration Group
2023-01-01

Abstract

Let pi be an irreducible unitary representation of a finitely generated non-abelian free group Gamma; suppose pi 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 Gamma 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.
2023
Free group representations from vector-valued multiplicative functions. III / Kuhn, M. G.; Saliani, S.; Steger, T.. - In: ISRAEL JOURNAL OF MATHEMATICS. - ISSN 0021-2172. - 258:1(2023), pp. 339-373. [10.1007/s11856-023-2474-z]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11388/322950
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