Quantum stiefel manifolds

Podkolzin and Vainerman claimed to prove that the*-algebra Sn,m q underlying SUq(n)/SUq (n - m) is the universal*-algebra given by a finite set of generators and relations. This can be used to show that C(SUq (n)/ SUq(n -m)) is the universal C*-algebra given by a finite set of generators and relations. But it appears that there is a mistake in the proof of the first claim which invalidates the latter claim. In this article, we establish in an independent way that C(SUq (n)/SUq (n - m)) can be defined by a finite set of generators and relations.