So is Polovetskaya or something like that? Then it seems as though the English adjectival form could well be Polovtsian, since we don't have that pesky K in there.

I remember from my youth that the standard spelling was Polovtsian but it was always pronounced Polovetsian (or Polovitsian).

Faldage, you are absolutely right! "A" for your Russian.
so the question now is what is the correct English form?
Polovtsian Dances?