2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/100929In 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.17 pagesQuantum AlgebraRepresentation Theory17B37; 20G42text