2004/10/28 by D. Shklyarov, Shklyarov, D., S. Sinel’shchikov +4
Mathematics · #20G42 #46L52 #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Quantum Algebra (math.QA) #math.QA #msc:20G42 #msc:46L52
paper · pdf · doi:10.48550/arxiv.math/0410605
LaTeX2e, 37 pages
arxiv created 2004/10/28 · openalex publication_date 2004/10/28 · arxiv updated 2016/09/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we study the Fock representation of a certain *-algebra which appears naturally in the framework of quantum group theory. It is also a generalization of the twisted CCR-algebra introduced by W. Pusz and S.~Woronowicz. We prove that the Fock representation is a faithful irreducible representation of the algebra by bounded operators in a Hilbert space, and, moreover, it is the only (up to unitary equivalence) representation possessing these properties. Keywords and phrases: Fock representation, quantum groups, bounded symmetric domain, non-compact Hermitian symmetric spaces