%0 Journal Article %T Regular functions on the Shilov boundary %A Olga Bershtein %J Mathematics %D 2004 %I arXiv %X 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. %U http://arxiv.org/abs/math/0411118v2