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

Neuhauser, Markus

Bull. Belg. Math. Soc. Simon Stevin, Tome 10 (2003) no. 1, p. 537-550 / Harvested from Project Euclid

Résumé

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.

Publié le : 2003-09-14
Classification: Kazhdan property, Kazhdan constant, bounded generation, topological groups, loop groups, 20G05, 22E67

@article{1070645800,
     author = {Neuhauser, Markus},
     title = {Kazhdan's Property T for the Symplectic Group over a Ring},
     journal = {Bull. Belg. Math. Soc. Simon Stevin},
     volume = {10},
     number = {1},
     year = {2003},
     pages = { 537-550},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1070645800}
}

Neuhauser, Markus. Kazhdan's Property T for the Symplectic Group over a Ring. Bull. Belg. Math. Soc. Simon Stevin, Tome 10 (2003) no. 1, pp.  537-550. http://gdmltest.u-ga.fr/item/1070645800/