Learn Dutch: Dat gezegd hebbende, liet de delegatie het document vertalen. - That having been said, the delegation had the document translated.

It is an absolute participial construction. hebbende is the present participle (the -end form) of hebben (to have). It combines with the past participle gezegd (said) to mean having said. The whole phrase Dat gezegd hebbende acts as a fixed rhetorical frame meaning having said that or that having been said.

Why does the verb liet come immediately after the comma?

In Dutch, the verb-second rule applies here. The entire participial phrase Dat gezegd hebbende occupies the first position in the sentence. Therefore, the main verb liet must take the second position, causing it to swap places with the subject de delegatie.

The English translation says had the document translated. Why does Dutch use the infinitive vertalen instead of a past participle like vertaald?

This is the Dutch causative construction. When you arrange for someone else to do a task, you use laten (here in the past tense as liet) plus the infinitive of the action verb. Unlike English, which uses have plus a past participle, Dutch always uses laten plus an infinitive, as in liet het document vertalen.

Is Dat gezegd hebbende something I would use in everyday casual conversation?