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

Huang, Gaofeng; Kutzschebauch, Frank; Schott, Josua (2024). Factorization of Holomorphic Matrices and Kazhdan's Property (T). Bulletin des sciences mathématiques, 190, p. 103376. Elsevier 10.1016/j.bulsci.2023.103376

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In this article we deduce some algebraic properties for the group Sp_{2n}(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 Ep_{2n}(O(X)) admits Kazhdan's property (T).

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