Regular functions on the Shilov boundary

Abstract

In this paper a quantum analog of the $\ast$-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 pages