Can someone explain to me what the 6 "recensions" of the Septuagint were? Also, how do we know about them? What sort of access do we have to each of them?
What is a Recension?
A recension is an edit on an existing work. For the Bible, this is usually distinct from a retranslation. If you were to take the KJV (1611) and simply remove the archaic language without working from the Hebrew and Greek, this would be a recension. A recension may also refer to a family of manuscripts. For example, the NT Alexandrian manuscript family could be called the Alexandrian recension as they all share common traits.
The original Septuagint was translated between the third and first century BC. However, beyond the Torah (translated first), it is almost impossible to determine the dates for individual books.
The Jewish Recensions
Sometime after this, three scholars separately revised the Greek against the Hebrew. We know about these from the writings of such men as Origen and Jerome.
Aquila (ca AD 130). Aquila used a very wooden style of translation. He preferred to go word-for-word from Hebrew into Greek. While this is helpful in determining the text he was working from, the resulting Greek is sometimes ambiguous. For example, Hebrew has separate verb forms for male and female subjects. Greek does not. Most translators would simply add a pronoun in places where the verb alone would not be enough to determine the subject. However, to remain at word-for-word, Aquila did not. Origen used his translation in one column of the Hexapla.
Symmachus (before AD 235). While the whole work is lost, pieces remain in the fragments of Origen's Hexapla where Symmachus' translation enjoyed a column. We can determine he used a more fluid style than Aquila. Some sources say Symmachus was an Ebionite Christian (sometimes called a Nazareen). Others that he was a Samaritan who converted to Judaism. His translation style allows him to express nuances available in Greek that are not in Hebrew. He also tried to be more literal than the Septuagint. Jerome used his work for comparison in places when working on the Vulgate. That is, Jerome worked from the Hebrew text but looked at how Symmachus had translated also.
Theodotion (ca. AD 150). He was a Hellenized Jew. Whether he worked from the Septuagint or the Hebrew texts (or even if he used a now lost tradition of the Hebrew Scriptures) is debated. His translation of Daniel was very popular among Christians. This work was one column of the Hexapla.
The Christian Recensions
Origen (ca AD 235). In one column of the Hexapla, Origen placed his own Greek version. This was both translation from Hebrew and text-critical analysis of the Greek to determine the best way to express the Scripture. The Hexapla is where we have most of these earlier recensions but even the Hexapla exists only in fragments today.
Lucian (before AD 312). Jerome mentions that Lucian revised the Septuagint. However, some scholars debate its existence. Jerome sometimes speaks well of the translation and other times disparages it. Lucian believed in the need for textual accuracy, and his work was popular in Asia and Syria and amongst such Greek Fathers as John Chrysostum. It exists in quotes of those fathers.
Hesychius (before AD 433). Little can be determined as only fragments remain (even fewer than the other above). What we do have shows he had a very allegorical hermeneutic and found entire reams of Christian theology in single verses of the Old Testament. More of his work survives in ancient libraries, however, there were numerous writers with the same first name and many scrolls have been stacked together. It would be a work worthy of several doctorates to go through the stacks and separate out the works of Hesychius of Jerusalem and those who carried his name.