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.
Citation
Markus Neuhauser. "Kazhdan's Property T for the Symplectic Group over a Ring." Bull. Belg. Math. Soc. Simon Stevin 10 (4) 537 - 550, December 2003. https://doi.org/10.36045/bbms/1070645800
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