A family of adapted complexifications for $S{L}_{2}\left(ℝ\right)$
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 5, Volume 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 $G=S{L}_{2}\left(ℝ\right)$ their realization as equivariant Riemann domains over ${G}^{ℂ}=S{L}_{2}\left(ℂ\right)$ 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, Serie 5, Volume 8 (2009) no. 1, pp. 17-49. http://www.numdam.org/item/ASNSP_2009_5_8_1_17_0/

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