Hi Luiz, "....,check the accuracy of the [analyses] and deductions of the author and repeat the investigation if they SO wish. '' In your example, "so" is an adverb to describe something that is done in more or less the way that is described earlier in a sentence. There is the verb "wish" and WHAT do "they" (other researchers) "wish" would happen? Well, they "wish" to "check the accuracy of the [analyses] and deductions of the author and repeat the investigation" which is described earlier in the sentence. Another example: "You can ask for a refund if you so wish." In this sentence, "so" again describes WHAT is being "wished" for (which is to get a refund). (You may have noticed a common structure (if+pronoun+so+wish) as well.) "You can ask for a refund if you wish (to)." has the same meaning as "You can ask for a refund if you so wish." because both "to" and "so" describe WHAT you wish to do. When someone does something if they "SO wish", the emphasis is on their freedom of choice, and when they would like to do it.

In this context, “so” is an adjective that modifies wish, and clarifies that “wish” refers to the action referred to elsewhere in the sentence (i.e., judging conclusions and checking accuracy). I don’t think the “so” is essential to the sentence, and the sentence could be written simply “if they wish.” But the so adds greater clarity, making clear that the sentence means “if they wish [to judge the conclusions, check the accuracy of the analyses and deductions of the author and repeat the investigation]. “So” takes the place of all the stuff in parentheses. Other examples, “You can come with me if you so wish.” “You can go on a tour at noon, or you can simply go to lunch if you so wish.”