Regular functions on the Shilov boundary

2004/11/05 by Olga Bershtein, Bershtein, Olga
Mathematics · #17B37 #20G42 #FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT) #math.QA #math.RT #msc:17B37 #msc:20G42

paper · pdf · doi:10.48550/arxiv.math/0411118

17 pages

arxiv created 2005/12/13 · arxiv updated 2009/12/01

Abstract

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.

Related

• Quantum Groups and Bounded Symmetric Domains
• Shilov boundary for "holomorphic functions" on a quantum matrix ball
• Spherical principal series of quantum Harish-Chandra modules
• The Shilov boundary for a q-analog of the holomorphic functions on the unit ball of 2 × 2 symmetric matrices
• Lectures on q-analogues of Cartan domains and associated Harish-Chandra modules