An analytic series of irreducible representations of the free group

Szwarc, Ryszard. "An analytic series of irreducible representations of the free group." Annales de l'institut Fourier 38.1 (1988): 87-110. <http://eudml.org/doc/74795>.

@article{Szwarc1988,
abstract = {Let $\{\bf F\}_ k$ be a free group on $k$ generators. We construct the series of uniformly bounded representations $\prod _ z$ of $\{\bf F\}_ k$ acting on the common Hilbert space, depending analytically on the complex parameter z, $1/(2k-1)&lt; \vert z\vert &lt; 1$, such that each representation $\prod _ z$ is irreducible. If $z$ is real or $\vert z\vert =1/(\sqrt\{2k-1\})$ then $\prod _ z$ is unitary; in other cases $\prod _ z$ cannot be made unitary. For $z\ne z^\{\prime \}$ representations $\prod _ z$ and $\prod _\{z^\{\prime \}\}$ are congruent modulo compact operators.},
author = {Szwarc, Ryszard},
journal = {Annales de l'institut Fourier},
keywords = {analytic series; free group; uniformly bounded representations; unitary representations; Hilbert spaces},
language = {eng},
number = {1},
pages = {87-110},
publisher = {Association des Annales de l'Institut Fourier},
title = {An analytic series of irreducible representations of the free group},
url = {http://eudml.org/doc/74795},
volume = {38},
year = {1988},
}

TY - JOUR
AU - Szwarc, Ryszard
TI - An analytic series of irreducible representations of the free group
JO - Annales de l'institut Fourier
PY - 1988
PB - Association des Annales de l'Institut Fourier
VL - 38
IS - 1
SP - 87
EP - 110
AB - Let ${\bf F}_ k$ be a free group on $k$ generators. We construct the series of uniformly bounded representations $\prod _ z$ of ${\bf F}_ k$ acting on the common Hilbert space, depending analytically on the complex parameter z, $1/(2k-1)&lt; \vert z\vert &lt; 1$, such that each representation $\prod _ z$ is irreducible. If $z$ is real or $\vert z\vert =1/(\sqrt{2k-1})$ then $\prod _ z$ is unitary; in other cases $\prod _ z$ cannot be made unitary. For $z\ne z^{\prime }$ representations $\prod _ z$ and $\prod _{z^{\prime }}$ are congruent modulo compact operators.
LA - eng
KW - analytic series; free group; uniformly bounded representations; unitary representations; Hilbert spaces
UR - http://eudml.org/doc/74795
ER -