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Fall 2011 Symmetry in tensor algebras over Hilbert space
Palle E. T. Jorgensen, Ilwoo Cho
Illinois J. Math. 55(3): 977-1013 (Fall 2011). DOI: 10.1215/ijm/1369841794


This paper deals with three issues: (1) Unitary representations $U$ of a scale of (finite and infinite dimensional) non-compact Lie groups $G(H)$ built on a fixed complex Hilbert space $H$; and their covariant systems. Our computations for these representations make use of the associated Lie algebras. (2) The covariant representations involve the $C^{*}$-algebras going by the names, the Toeplitz algebras, and the Cuntz algebras. (3) An essential result which also is used throughout is our computation of the commutant of the unitary representation $U$ of $G(H)$ mentioned in (1). For a fixed Hilbert space $H$, we apportion the commutant as a specific projective limit-algebra of operators.


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Palle E. T. Jorgensen. Ilwoo Cho. "Symmetry in tensor algebras over Hilbert space." Illinois J. Math. 55 (3) 977 - 1013, Fall 2011.


Published: Fall 2011
First available in Project Euclid: 29 May 2013

zbMATH: 1268.05234
MathSciNet: MR3069293
Digital Object Identifier: 10.1215/ijm/1369841794

Primary: 05E18 , 11F70 , 37C45 , 37C80 , 46L54 , 47L30 , 47L90

Rights: Copyright © 2011 University of Illinois at Urbana-Champaign


Vol.55 • No. 3 • Fall 2011
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