Degenerate principal series of quantum Harish-Chandra modules over U_qsp₄(R)

Abstract:
We investigate a quantum analogue of a degenerate principal series of U_qsp₄(R)-modules (0<q<1) related to the Shilov boundary of the quantum symmetric 2×2-matrix unit ball. We give necessary and sufficient conditions for the modules to be simple and unitarizable. These results are q-analogues of known classical results on reducibility and unitarizability of SP₄(R)-modules obtained by Johnson, Zhang, Howe and Tan.