A family of adapted complexifications for SL 2 ()
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 8 (2009) no. 1, p. 17-49
Let G be a non-compact, real semisimple Lie group. We consider maximal complexifications of G which are adapted to a distinguished one-parameter family of naturally reductive, left-invariant metrics. In the case of G=SL 2 () their realization as equivariant Riemann domains over G =SL 2 () is carried out and their complex-geometric properties are investigated. One obtains new examples of non-univalent, non-Stein, maximal adapted complexifications.
Classification:  53C30,  53C22,  32C09,  32Q99,  32M05
@article{ASNSP_2009_5_8_1_17_0,
     author = {Halverscheid, Stefan and Iannuzzi, Andrea},
     title = {A family of adapted complexifications for $SL\_2(\mathbb{R})$},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     publisher = {Scuola Normale Superiore, Pisa},
     volume = {Ser. 5, 8},
     number = {1},
     year = {2009},
     pages = {17-49},
     zbl = {1180.53053},
     mrnumber = {2512199},
     language = {en},
     url = {http://www.numdam.org/item/ASNSP_2009_5_8_1_17_0}
}
Halverscheid, Stefan; Iannuzzi, Andrea. A family of adapted complexifications for $SL_2(\mathbb{R})$. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 5, Tome 8 (2009) no. 1, pp. 17-49. https://www.numdam.org/item/ASNSP_2009_5_8_1_17_0/

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