On Kazhdan's Property (T) for the special linear group of holomorphic functions

Björn Ivarsson; Frank Kutzschebauch

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arXiv · 1202.6531

On Kazhdan's Property (T) for the special linear group of holomorphic functions

Björn Ivarsson·Frank Kutzschebauch

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Abstract

We investigate when the group $SL_n(\mathcal{O}(X))$ of holomorphic maps from a Stein space $X$ to $SL_n (\C)$ has Kazhdan's property (T) for $n\ge 3$. 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 $n\ge 3$. 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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Björn Ivarsson, Frank Kutzschebauch. 2012-02-29. On Kazhdan's Property (T) for the special linear group of holomorphic functions. https://arxiv.org/abs/1202.6531

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