Olga Bershtein (Institute for Low Temperature Physics and Engineering, Kharkov, Ukraine)

Degenerate principal series of quantum Harish-Chandra modules over Uqsp4(R)

We investigate a quantum analogue of a degenerate principal series of Uqsp4(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.