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Fock Representations and Quantum Matrices

D. Shklyarov·S. Sinel'shchikov·L. Vaksman
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Abstract

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

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BibTeXRIS

D. Shklyarov, S. Sinel'shchikov, L. Vaksman. 2004-10-28. Fock Representations and Quantum Matrices. https://arxiv.org/abs/math/0410605

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