Let be a free group on generators. We construct the series of uniformly bounded representations of acting on the common Hilbert space, depending analytically on the complex parameter z, , such that each representation is irreducible. If is real or then is unitary; in other cases cannot be made unitary. For representations and are congruent modulo compact operators.
Soit un groupe libre avec générateurs. On construit une série des représentations uniformément bornées de qui opèrent sur un espace de Hilbert commun. Les représentations sont irréductibles et dépendent analytiquement d’un paramètre complexe tel que . Pour réel ou les sont unitaires; autrement ne sont pas unitarisables. Pour les différences sont des opérateurs compacts.
@article{AIF_1988__38_1_87_0, author = {Szwarc, Ryszard}, title = {An analytic series of irreducible representations of the free group}, journal = {Annales de l'Institut Fourier}, pages = {87--110}, publisher = {Institut Fourier}, address = {Grenoble}, volume = {38}, number = {1}, year = {1988}, doi = {10.5802/aif.1124}, mrnumber = {89j:22023}, zbl = {0634.22003}, language = {en}, url = {http://www.numdam.org/articles/10.5802/aif.1124/} }
TY - JOUR AU - Szwarc, Ryszard TI - An analytic series of irreducible representations of the free group JO - Annales de l'Institut Fourier PY - 1988 SP - 87 EP - 110 VL - 38 IS - 1 PB - Institut Fourier PP - Grenoble UR - http://www.numdam.org/articles/10.5802/aif.1124/ DO - 10.5802/aif.1124 LA - en ID - AIF_1988__38_1_87_0 ER -
%0 Journal Article %A Szwarc, Ryszard %T An analytic series of irreducible representations of the free group %J Annales de l'Institut Fourier %D 1988 %P 87-110 %V 38 %N 1 %I Institut Fourier %C Grenoble %U http://www.numdam.org/articles/10.5802/aif.1124/ %R 10.5802/aif.1124 %G en %F AIF_1988__38_1_87_0
Szwarc, Ryszard. An analytic series of irreducible representations of the free group. Annales de l'Institut Fourier, Volume 38 (1988) no. 1, pp. 87-110. doi : 10.5802/aif.1124. http://www.numdam.org/articles/10.5802/aif.1124/
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