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An analytic family of uniformly bounded representations of free products of discrete groups. (English) Zbl 0742.30038

We construct for each \(| z|<1\) a uniformly bounded representation \(\pi_ z\) of a free product group. The correspondence \(z\mapsto\pi_ z\) is proved to be analytic. The representations are irreducible if the free product factors are infinite groups. On free groups they have as coefficients block radial functions — this gives thus a new series of representations. They can be made unitary iff \(z\in(-{1 \over N-1},1)\).

MSC:

30F35 Fuchsian groups and automorphic functions (aspects of compact Riemann surfaces and uniformization)
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