no. 2
Geometry of biinvariant subsets of complex semisimple Lie groups
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Tome 26 (1998) no. 2, pp. 329-356. 
@article{ASNSP_1998_4_26_2_329_0,
     author = {Fels, Gregor and Geatti, Laura},
     title = {Geometry of biinvariant subsets of complex semisimple Lie groups},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     pages = {329--356},
     publisher = {Scuola normale superiore},
     volume = {Ser. 4, 26},
     number = {2},
     year = {1998},
     zbl = {0922.32011},
     mrnumber = {1631593},
     language = {en},
     url = {www.numdam.org/item/ASNSP_1998_4_26_2_329_0/}
}
Fels, Gregor; Geatti, Laura. Geometry of biinvariant subsets of complex semisimple Lie groups. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Série 4, Tome 26 (1998) no. 2, pp. 329-356. http://www.numdam.org/item/ASNSP_1998_4_26_2_329_0/

[Bo] A. Boggess, CR-Manifolds and Tangential Cauchy-Riemann Complex, Studies in Advanced Math., C.R.C. Press, 1991. | MR 1211412 | Zbl 0760.32001

[Br] R. Bremigan, Invariant analytic domains in complex semisimple groups, Transformation Groups 1 (1996), 279-305. | MR 1424446 | Zbl 0867.22004

[FH] G. Fels - A.T. Huckleberry, A Characterisation of K-Invariant Stein Domains in Symmetric Embeddings, Complex Analysis and Geometry, Plenum Press, New York, 1993, 223-234. | MR 1211883 | Zbl 0790.32030

[Gr] S.J. Greenfield, Cauchy-Riemann equations in several complex variables, Ann. Scuola Norm. Sup. Pisa 22 (1968), 257-314. | Numdam | MR 237816 | Zbl 0159.37502

[GG] I.M. Gelfand - S.G. Gindikin, Complex manifolds whose skeletons are semisimple real Lie groups, and analytic discrete series of representations, Functional Anal. Appl. 7-4 (1977), 19-27. | MR 492076 | Zbl 0444.22006

[HN] J. Hilgert - K.H. Neeb, Lie Semigroups and their Applications, Lecture Notes in Math. 1552, Springer Verlag, 1993. | MR 1317811 | Zbl 0807.22001

[Hu] J.E. Humphreys, Conjugacy Classes in Semisimple Algebraic Groups, Mathematical Surveys and Monographs, Vol. 43, AMS, Providence, Rhole Island, 1995. | MR 1343976 | Zbl 0834.20048

[Las] M. Lassalle, Séries de Laurent des fonctions holomorphes dans la complexification d'une espace symétrique compact, Ann. Sci. École Norm. Sup. 4 (1973), 267-290. | Numdam | Zbl 0452.43011

[L1] J.J. Loeb, Plurisubharmonicité et convexité sur les groupes reductifs complexes, Pub. IRMA-Lille 2 VIII (1986), 1-12.

[L2] J.J. Loeb, Action d'une forme réelle d'un groupe de Lie complexe sur les fonctions plurisubharmoniques, Ann. Inst. Fourier 35 (1985), 59-97. | Numdam | MR 812319 | Zbl 0563.32013

[MO] T. Matsuki - T. Oshima, Orbits of affine symmetric spaces under the action of the isotropy groups, J. Math. Soc. Japan 32 (1980), 399-414. | MR 567427 | Zbl 0451.53039

[N1] K.H. Neeb, Invariant convex sets and functions in Lie Algebras, Semigroups Forum 53 (1996), 305-349. | MR 1400650 | Zbl 0873.17009

[N2] K.H. Neeb, On the Complex and Convex Geometry of Ol'shanskiĭ semigroups, preprint 10, Institut Mittag-Leffler, 1995/ 96. | MR 1614894

[O1] G I. OL'SHANSKIĭ, Invariant cones in Lie algebras, Lie semigroups, and the holomorphic discrete series, Functional Anal. Appl. 15 (1982), 275-285. | MR 639200 | Zbl 0503.22011

[O2] G.I. Ol'Shanski, Complex Lie semigroups, Hardy spaces and the program of Gelfand Gindikin, Differential Geom. Appl. 1 (1982), 235-246. | MR 1244445 | Zbl 0789.22011

[Ra] P.K. Rashevskij, On the connectedness of the fixed point set of an automorphism of a Lie group, Funct. Anal. Appl. 6 (1973), 341-342. | Zbl 0285.54036

[St] R.J. Stanton, Analytic extension of the holomorphic discrete series, Amer. J. Math. 108 (1986), 1411-1424. | MR 868896 | Zbl 0626.43008

[Su] M. Sugiura, Conjugate classes of Cartan subalgebras in real semisimple Lie Algebras, J. Math. Soc. Japan 11 (1959), 374-434. | MR 146305 | Zbl 0204.04201

[Tu] A.E. Tumanov, The geometry of CR-Manifolds, Encyclopaedia of Mathematical Sciences, Vol. 9, Springer Verlag, 1989, 201-221. | Zbl 0658.32007