Generators of the Odd Dimensional Quantum Spheres

As is well-known, the $(2N-1)$-quantum sphere $S^{2N-1}_q$ is defined to be the invariant subalgebra of $SU_q(N)$ under the coaction $\Delta_R = (id \otimes \pi) \circ \Delta$, where $\Delta$ is the comultiplication of $SU_q(N)$, and $\pi: SU_q(N) \to U_q(N-1)$ is the Hopf algebra surjection defined by setting, for $i,j \neq 1$, $\pi(u^i_1)=\pi(u^1_j)=0$, $\pi(u^1_1)$ = det$_q^{-1}$, and $\pi (u^i_j) = u^{i-1}_{j-1}$. (Recall that the invariant subalgebra of a $H$-coaction $\Delta_R$ on vector space $V$ is the subspace of all elements $v$ for which $\Delta_R(v) = v \otimes 1$.) An oft quoted result is that $S^{2N-1}_q$ is generated, as an algebra, by the elements $u^i, S(u^1_i)$, for $i=1, \ldots N$. Now it is clear that these elements are invariant, but it is far from clear (at least to me) that generate all the invariant subspace. Can anyone see why? The usual references given are in Russian and, even at that, are unavailable on the web.