On a Family of Representations of Residually Finite Groups
Tóm tắt
For a residually finite group G, its normal subgroups G ⊃ G1 ⊃ G2⋯ with
$\cap _{n\in \mathbb N}G_{n}=\{e\}$
and for a growth function γ we construct a unitary representation πγ of G. For the minimal growth, πγ is weakly equivalent to the regular representation, and for the maximal growth it is weakly equivalent to the direct sum of the quasiregular representations on the quotients G/Gn. In the case of intermediate growth we show two examples of different behaviour of πγ.
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