标题： Borel--Serre 型边界化和环群的规范对 显示英文标题

标题： Borel--Serre type bordifications and Canonical Pairs for Loop groups

摘要： 针对实环群的(正半部分)对称空间，我们附加了一个类似Borel--Serre的边界化，并为其配备了一个Hausdorff拓扑。 附加的边界由环群的某些有理抛物线索引，被证明同伦于一个仿射的、有理的Tits建筑。 还证明了环群的一个类似数论群的结构在边界化上连续作用，其商通过H. Garland的约化理论进行研究。 虽然商不再是紧致的（与有限维情况下的Borel--Serre构造不同），但我们将其非紧性与环群的中心联系起来。 我们还引入了环群的半稳定性概念，这受到Harder--Narasimhan、Behrend以及最近的Chaudouard工作的启发，并利用这一概念描述了我们的环对称空间的划分。 该划分随后与有理边界化及其商相关联。 显示英文摘要

摘要： To the symmetric space of the (positive half) of a real loop group, we attach a Borel--Serre type bordification and equip it with a Hausdorff topology. The attached boundary, indexed by certain rational parabolics of the loop group, is shown to be homotopic to an affine, rational Tits building. A loop analogue of an arithmetic group is also shown to act continuously on the bordification and its quotient by this action is studied using the reduction theory of H. Garland. While the quotient is no longer compact (as in the Borel--Serre construction from finite-dimensions) we relate the non-compactness to the center of the loop group. We also introduce a notion of semi-stability for loop groups, following works of Harder--Narasimhan, Behrend, and most recently Chaudouard, and use this to describe a partition of our loop symmetric space. This partition is then related to the rational bordification and its quotient.