  In this paper a quantum analog of the $*$-algebra of regular functions on the
Shilov boundary $S(\mathbb D)$ of bounded symmetric domain $\mathbb D$ is
constructed. The algebras of regular functions on $S(\mathbb D)$ are described
in terms of generators and relations for two particular series of bounded
symmetric domains. Also, the degenerate principal series of quantum
Harich-Chandra modules related to $S(\mathbb D)=U_n$ is investigated.
