A new axiomatics for masures

Abstract

Masures are generalizations of Bruhat-Tits buildings. They were introduced to study Kac-Moody groups over ultrametric fields, which generalize reductive groups over the same fields. If A and A are two apartments in a building, their intersection is convex (as a subset of the finite dimensional affine space A) and there exists an isomorphism from A to A fixing this intersection. We study this question for masures and prove that the analogous statement is true in some particular cases. We deduce a new axiomatic of masures, simpler than the one given by Rousseau.

This paper was initially called "Convexity in a masure"

References in corpus (6)

• Iwahori-Hecke algebras for Kac-Moody groups over local fields
• Macdonald's formula for Kac-Moody groups over local fields
• Gindikin-Karpelevich finiteness for Kac-Moody groups over local fields
• Distances on a masure (affine ordered hovel)
• Kac-Moody symmetric spaces
• Completed Iwahori-Hecke algebras and parahoric Hecke algebras for Kac-Moody groups over local fields

Cited by in corpus (4)

• A new axiomatics for masures II
• Twin masures associated with Kac-Moody groups over Laurent polynomials
• On structure constants of Iwahori-Hecke algebras for Kac-Moody groups
• Topologies on split Kac-Moody groups over valued fields