Update
The Columbia student paper reports that sororities will get "stage one" (not full) recognition, followed by other steps toward full recognition. Apparently the main significance of all this, at least at present, is use of facilities, some funding, ability to publicize on Barnard's campus, and so on.
The complexities of student group funding at Barnard, as well as the relationship between Columbia and Barnard, are not my field of expertise at all, so read the article (link below) and any posts we get from people who know what is what on those campuses.
http://www.columbiaspectator.com/201...ion-sororities