Borel-Serre type constructions for Loop Groups

Joint work with Punya Satpathy

For a reductive group G, Borel and Serre introduced a compactification of a large class of arithmetic quotients of the symmetric space attached to G. After reviewing some aspects of their construction, we explain how to generalize it to the case when G is replaced by an infinite-dimensional analogue LG, the loop group of G. Along the way, we describe  a partition of an arithmetic quotient of LG, inspired by the work of P.-H. Chaudouard for GL_n and related to earlier constructions of Harder-Narasimhan and Behrend.