Almost split Kac-Moody groups over ultrametric fields

Guy Rousseau (1)

1 IECL - Institut Élie Cartan de Lorraine

For a split Kac-Moody group G over an ultrametric field K, S. Gaussent and the author defined an ordered affine hovel on which the group acts; it generalizes the Bruhat-Tits building which corresponds to the case when G is reductive. This construction was generalized by C. Charignon to the almost split case when K is a local field. We explain here these constructions with more details and prove many new properties e.g. that the hovel of an almost split Kac-Moody group is an ordered affine hovel, as defined in a previous article.

Mots clés: building; local field; Kac-Moody group; hovel

Domaines: Théorie des groupes [math.GR]

Guy Rousseau. Almost split Kac-Moody groups over ultrametric fields. Groups, Geometry, and Dynamics, 2017, 11, pp.891-975. ⟨10.4171/ggd/418⟩. ⟨hal-00674912v2⟩