  In this paper we study a quantum analogue of a degenerate principal series of
$U_q \mathfrak{su}_{n,n}$-modules ($0<q<1$) related to the Shilov boundary of
the quantum $n \times n$-matrix unit ball. We give necessary and sufficient
conditions for the modules to be simple and unitarizable and investigate their
equivalence.
  These results are q-analogues of known classical results on reducibility and
unitarizability of SU(n,n)-modules obtained by Johnson, Sahi, Zhang, Howe and
Tan.
