In 2004 the second and third authors introduced a large family of representations of a free group Gamma weakly contained in the regular representation.In this paper we enlarge a little bit this class for Gamma so that the new class Mult(Gamma), of the multiplicative representations, is stable under taking finite direct sums, under restriction to, and induction from a finite index subgroup.As an application, using the properties of multiplicative representations we define a new class of tempered unitary representations for a class of groups that includes for example all lattices of unimodular subgroups of automorphisms of a locally finite regular tree.The main tool is the detailed study of the properties of the action of a free group on its Cayley graph with respect to a change of generators, as well as the relative properties of the action of a subgroup of finite index after the choice of a nice fundamental domain.
Stability properties of multiplicative representations of the free group / Iozzi, A.; Kuhn, M. G.; Steger, T.. - In: TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY. - ISSN 0002-9947. - 371:12(2019), pp. 8699-8731. [10.1090/tran/7552]
Stability properties of multiplicative representations of the free group
Steger T.Membro del Collaboration Group
2019-01-01
Abstract
In 2004 the second and third authors introduced a large family of representations of a free group Gamma weakly contained in the regular representation.In this paper we enlarge a little bit this class for Gamma so that the new class Mult(Gamma), of the multiplicative representations, is stable under taking finite direct sums, under restriction to, and induction from a finite index subgroup.As an application, using the properties of multiplicative representations we define a new class of tempered unitary representations for a class of groups that includes for example all lattices of unimodular subgroups of automorphisms of a locally finite regular tree.The main tool is the detailed study of the properties of the action of a free group on its Cayley graph with respect to a change of generators, as well as the relative properties of the action of a subgroup of finite index after the choice of a nice fundamental domain.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.