In this note, we prove that a two-spherical Kac–Moody group over a local field endowed with the Kac–Peterson topology enjoys Kazhdan's property (T).
The authors thank Jan Dymara, Tsachik Gelander and Pierre de la Harpe for helpful discussions on Kac–Moody groups and Kazhdan's property (T). They also thank Institut Mittag-Leffler (Djursholm, Sweden) and Mathematisches Forschungsinstitut Oberwolfach for their hospitality during the preparation of this note. Finally, they thank Pierre-Emmanuel Caprace and an anonymous referee for helpful comments on an earlier version of this note.
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