论文标题
Drinfeld对称空间的可逆分析功能和Steinberg表示的通用扩展
Invertible analytic functions on Drinfeld symmetric spaces and universal extensions of Steinberg representations
论文作者
论文摘要
最近，Gekeler证明了Drinfeld上半部空间上的可逆分析函数组模量函数与整体广义Steinberg表示的双重形态是同构。在本说明中，我们表明，可逆函数组是该Steinberg表示的通用延伸的双重偶数。作为一种应用，我们表明，在达尔蒙（Darmon）意义上，可以根据$ \ Mathcal {l} $来计算Hilbert模块化形式的刚性分析性theta theta cocycles的障碍物 - 相关Galois表示的不变性。同样的论点适用于确定的统一群体的theta Cocycles。
Recently, Gekeler proved that the group of invertible analytic functions modulo constant functions on Drinfeld's upper half space is isomorphic to the dual of an integral generalized Steinberg representation. In this note we show that the group of invertible functions is the dual of a universal extension of that Steinberg representation. As an application, we show that lifting obstructions of rigid analytic theta cocycles of Hilbert modular forms in the sense of Darmon--Vonk can be computed in terms of $\mathcal{L}$-invariants of the associated Galois representation. The same argument applies to theta cocycles for definite unitary groups.
