TY - JOUR
AU1 - Kuhn, M. Gabriella
AU2 - Saliani, Sandra
AU3 - Steger, Tim
AB - Let π be an irreducible unitary representation of a finitely generated non-abelian 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.
TI - Free group representations from vector-valued multiplicative functions. III
JF - Israel Journal of Mathematics
DO - 10.1007/s11856-023-2474-z
DA - 2023-12-01
UR - https://www.deepdyve.com/lp/springer-journals/free-group-representations-from-vector-valued-multiplicative-functions-yBoNwCXOkQ
SP - 339
EP - 373
VL - 258
IS - 1
DP - DeepDyve
ER -