We investigate when the group SLn(O(X)) of holomorphic maps from
a Stein space X to SL_n (\C) has Kazhdan's property (T) for n≥3. This
provides a new class of examples of non-locally compact groups having Kazhdan's
property (T). In particular we prove that the holomorphic loop group of SL_n
(\C) has Kazhdan's property (T) for n≥3. Our result relies on the method
of Shalom to prove Kazhdan's property (T) and the solution to Gromov's
Vaserstein problem by the authors.Comment: 5 page