In this paper we study a quantum analogue of a degenerate principal series of
Uq​sun,n​-modules (0<q<1) related to the Shilov boundary of
the quantum nĂ—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.Comment: 33 pages, 4 figure