Classification of connected unimodular Lie groups with discrete series
Annales de l'Institut Fourier, Tome 30 (1980) no. 1, pp. 159-192.

On introduit la classe des H-groupes, intermédiaire entre celle des groupes de Lie connexes nilpotents et celle des groupes de Lie connexes résolubles. Soit G un groupe de Lie connexe unimodulaire, de centre Z, tel que G/ Rad G ait un centre fini. A quelques restrictions techniques près, on montre qu’un tel groupe G a une série discrète de représentations si et seulement s’il se représente sous la forme G=HS avec les hypothèses suivantes : a) H est un H-groupe de centre Z 0 ; b) S est un groupe de Lie réductif connexe, possédant une série discrète; c) Cent(S)/Z est compact; d) on a HS=Z 0 .

We introduce a new class of connected solvable Lie groups called H-group. Namely a H-group is a unimodular connected solvable Lie group with center Z such that for some in the Lie algebra h of H, the symplectic for B on h/z given by ([x,y]) is nondegenerate. Moreover, apart form some technical requirements, it will be proved that a connected unimodular Lie group G with center Z, such that the center of G/ Rad G is finite, has discrete series if and only if G may be written as G=HS , HS=Z 0 , where H is a H-group with center Z 0 and S is a connected reductive Lie group with discrete series such that Cent(S)/Z is compact.

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     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},
     mrnumber = {82a:22016},
     zbl = {0418.22010},
     language = {en},
     url = {http://www.numdam.org/articles/10.5802/aif.779/}
}
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Anh Nguyen Huu. Classification of connected unimodular Lie groups with discrete series. Annales de l'Institut Fourier, Tome 30 (1980) no. 1, pp. 159-192. doi : 10.5802/aif.779. http://www.numdam.org/articles/10.5802/aif.779/

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