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LSpice
LSpice
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I do not have access to the article you are citing but iI have made a little search and iI think the answer to your question is yes (given that we are speaking about a non-compact, connected, semisimple Lie group $G$).
You can find the proof in a previous article by the same author. See: Kaehler coherent state orbits for representations of semisimple Lie groupsLisiecki - Kaehler coherent state orbits for representations of semisimple Lie groups (it is proposition 3.3, p. 251).

I do not have access to the article you are citing but i have made a little search and i think the answer to your question is yes (given that we are speaking about a non-compact, connected, semisimple Lie group $G$).
You can find the proof in a previous article by the same author. See: Kaehler coherent state orbits for representations of semisimple Lie groups (it is proposition 3.3, p. 251)

I do not have access to the article you are citing but I have made a little search and I think the answer to your question is yes (given that we are speaking about a non-compact, connected, semisimple Lie group $G$).
You can find the proof in a previous article by the same author. See: Lisiecki - Kaehler coherent state orbits for representations of semisimple Lie groups (it is proposition 3.3, p. 251).

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Konstantinos Kanakoglou
Konstantinos Kanakoglou
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I do not have access to the article you are citing but i have made a little search and i think the answer to your question is yes (given that we are speaking about a non-compact, connected, semisimple Lie group $G$).
You can find the proof in a previous article by the same author. See: Kaehler coherent state orbits for representations of semisimple Lie groups (it is proposition 3.3, p. 251)