## Bulletin of the Belgian Mathematical Society - Simon Stevin

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

Markus Neuhauser

#### 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

https://projecteuclid.org/euclid.bbms/1070645800

Digital Object Identifier
doi:10.36045/bbms/1070645800

Mathematical Reviews number (MathSciNet)
MR2040529

Zentralblatt MATH identifier
1063.22021

#### 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