Abstract
We investigate when the group SLn (O(X)) of holomorphic maps from a Stein space X to SLn (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 SLn (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.
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More From: Bulletin of The Belgian Mathematical Society-simon Stevin
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