论文标题
全体形态矩阵和卡兹丹财产的分解（t）
Factorization of Holomorphic Matrices and Kazhdan's property (T)
论文作者
论文摘要
在本文中，我们为组$ \ mathrm {sp} _ {2n}（\ Mathcal {o}（x））$ holomorthic sompletictic矩阵$ x $ x $ x $：HOLOMORPHICICIADIAD：HOLOMORPHICINCIATION，指定性分支，指定性分支和Kazhdan的属性（T）。在全体形态分解中，我们结合了第三作者和K理论工具的最新结果，以在$ x $是一维或二维的情况下为案例提供明确的界限。接下来，我们使用它们来找到指数分解的界限。作为进一步的应用程序，我们表明基本符号组$ \ mathrm {ep} _ {2n}（\ Mathcal {o}（x）（x））$ ADGEND KAZHDAN的属性（t）。
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).
