Factorization of Holomorphic Matrices and Kazhdan's property (T)

Gaofeng Huang; Frank Kutzschebauch; Josua Schott

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arXiv · 2207.12057

Factorization of Holomorphic Matrices and Kazhdan's property (T)

Gaofeng Huang·Frank Kutzschebauch·Josua Schott

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Abstract

In this article we deduce some algebraic properties for the group $\mathrm{Sp}_{2n} (\mathcal{O}(X))$ of holomorphic symplectic matrices on a Stein space $X$: holomorphic factorization, exponential factorization, and Kazhdan's property (T). In holomorphic factorization we combine a recent result of the third author and K-theory tools to give explicit bounds for the case when $X$ is one-dimensional or two-dimensional. Next we use them to find bounds for exponential factorization. As a further application, we show that the elementary symplectic group $\mathrm{Ep}_{2n}(\mathcal{O}(X))$ admits Kazhdan's property (T).

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Gaofeng Huang, Frank Kutzschebauch, Josua Schott. 2022-07-25. Factorization of Holomorphic Matrices and Kazhdan's property (T). https://arxiv.org/abs/2207.12057

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