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february 2014 On Kazhdan's Property (T) for the special linear group of holomorphic functions
Björn Ivarsson, Frank Kutzschebauch
Bull. Belg. Math. Soc. Simon Stevin 21(1): 185-191 (february 2014). DOI: 10.36045/bbms/1394544304

Abstract

We investigate when the group $\mbox{SL}_n(\mathcal{O}(X))$ of holomorphic maps from a Stein space $X$ to $\mbox{SL}_n (\C)$ 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 $\mbox{SL}_n (\C)$ 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. "On Kazhdan's Property (T) for the special linear group of holomorphic functions." Bull. Belg. Math. Soc. Simon Stevin 21 (1) 185 - 191, february 2014. https://doi.org/10.36045/bbms/1394544304

Information

Published: february 2014
First available in Project Euclid: 11 March 2014

zbMATH: 1315.22006
MathSciNet: MR3178540
Digital Object Identifier: 10.36045/bbms/1394544304

Subjects:
Primary: 18F25, 32M05
Secondary: 22D10, 32M25

Rights: Copyright © 2014 The Belgian Mathematical Society

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Vol.21 • No. 1 • february 2014
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