We introduce a new class of connected solvable Lie groups called -group. Namely a -group is a unimodular connected solvable Lie group with center such that for some in the Lie algebra of , the symplectic for on given by is nondegenerate. Moreover, apart form some technical requirements, it will be proved that a connected unimodular Lie group with center , such that the center of is finite, has discrete series if and only if may be written as , , where is a -group with center and is a connected reductive Lie group with discrete series such that Cent is compact.
On introduit la classe des -groupes, intermédiaire entre celle des groupes de Lie connexes nilpotents et celle des groupes de Lie connexes résolubles. Soit un groupe de Lie connexe unimodulaire, de centre , tel que ait un centre fini. A quelques restrictions techniques près, on montre qu’un tel groupe a une série discrète de représentations si et seulement s’il se représente sous la forme avec les hypothèses suivantes : a) est un -groupe de centre ; b) est un groupe de Lie réductif connexe, possédant une série discrète; c) Cent est compact; d) on a .
@article{AIF_1980__30_1_159_0, author = {Anh Nguyen Huu}, title = {Classification of connected unimodular {Lie} groups with discrete series}, journal = {Annales de l'Institut Fourier}, pages = {159--192}, publisher = {Institut Fourier}, address = {Grenoble}, volume = {30}, number = {1}, year = {1980}, doi = {10.5802/aif.779}, zbl = {0418.22010}, mrnumber = {82a:22016}, language = {en}, url = {https://aif.centre-mersenne.org/articles/10.5802/aif.779/} }
TY - JOUR AU - Anh Nguyen Huu TI - Classification of connected unimodular Lie groups with discrete series JO - Annales de l'Institut Fourier PY - 1980 SP - 159 EP - 192 VL - 30 IS - 1 PB - Institut Fourier PP - Grenoble UR - https://aif.centre-mersenne.org/articles/10.5802/aif.779/ DO - 10.5802/aif.779 LA - en ID - AIF_1980__30_1_159_0 ER -
%0 Journal Article %A Anh Nguyen Huu %T Classification of connected unimodular Lie groups with discrete series %J Annales de l'Institut Fourier %D 1980 %P 159-192 %V 30 %N 1 %I Institut Fourier %C Grenoble %U https://aif.centre-mersenne.org/articles/10.5802/aif.779/ %R 10.5802/aif.779 %G en %F AIF_1980__30_1_159_0
Anh Nguyen Huu. Classification of connected unimodular Lie groups with discrete series. Annales de l'Institut Fourier, Volume 30 (1980) no. 1, pp. 159-192. doi : 10.5802/aif.779. https://aif.centre-mersenne.org/articles/10.5802/aif.779/
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