Bulletin of the Belgian Mathematical Society - Simon Stevin

Kazhdan's Property T for the Symplectic Group over a Ring

Markus Neuhauser

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Abstract

Kazhdan constants for $\mathop{\rm {Sp}}\left( n,\Omega \right) $ where $\Omega $ is a commutative topological ring with dense finitely generated subring with unity are determined. This implies Kazhdan's property T for these groups. As application explicit Kazhdan constants are determined for the loop groups corresponding to $\mathop{\rm {Sp}}\left( n,\mathbf{C}\right) $. These are further examples of groups with property T which are infinite dimensional Lie groups and not locally compact.

Article information

Source
Bull. Belg. Math. Soc. Simon Stevin, Volume 10, Number 4 (2003), 537-550.

Dates
First available in Project Euclid: 5 December 2003

Permanent link to this document
https://projecteuclid.org/euclid.bbms/1070645800

Digital Object Identifier
doi:10.36045/bbms/1070645800

Mathematical Reviews number (MathSciNet)
MR2040529

Zentralblatt MATH identifier
1063.22021

Subjects
Primary: 20G05: Representation theory 22E67: Loop groups and related constructions, group-theoretic treatment [See also 58D05]

Keywords
Kazhdan property Kazhdan constant bounded generation topological groups loop groups

Citation

Neuhauser, Markus. Kazhdan's Property T for the Symplectic Group over a Ring. Bull. Belg. Math. Soc. Simon Stevin 10 (2003), no. 4, 537--550. doi:10.36045/bbms/1070645800. https://projecteuclid.org/euclid.bbms/1070645800


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